ScalarEvolution.cpp revision b2840fdcd8a98de32e86e70a267b54cf0af35140
1//===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===// 2// 3// The LLVM Compiler Infrastructure 4// 5// This file is distributed under the University of Illinois Open Source 6// License. See LICENSE.TXT for details. 7// 8//===----------------------------------------------------------------------===// 9// 10// This file contains the implementation of the scalar evolution analysis 11// engine, which is used primarily to analyze expressions involving induction 12// variables in loops. 13// 14// There are several aspects to this library. First is the representation of 15// scalar expressions, which are represented as subclasses of the SCEV class. 16// These classes are used to represent certain types of subexpressions that we 17// can handle. We only create one SCEV of a particular shape, so 18// pointer-comparisons for equality are legal. 19// 20// One important aspect of the SCEV objects is that they are never cyclic, even 21// if there is a cycle in the dataflow for an expression (ie, a PHI node). If 22// the PHI node is one of the idioms that we can represent (e.g., a polynomial 23// recurrence) then we represent it directly as a recurrence node, otherwise we 24// represent it as a SCEVUnknown node. 25// 26// In addition to being able to represent expressions of various types, we also 27// have folders that are used to build the *canonical* representation for a 28// particular expression. These folders are capable of using a variety of 29// rewrite rules to simplify the expressions. 30// 31// Once the folders are defined, we can implement the more interesting 32// higher-level code, such as the code that recognizes PHI nodes of various 33// types, computes the execution count of a loop, etc. 34// 35// TODO: We should use these routines and value representations to implement 36// dependence analysis! 37// 38//===----------------------------------------------------------------------===// 39// 40// There are several good references for the techniques used in this analysis. 41// 42// Chains of recurrences -- a method to expedite the evaluation 43// of closed-form functions 44// Olaf Bachmann, Paul S. Wang, Eugene V. Zima 45// 46// On computational properties of chains of recurrences 47// Eugene V. Zima 48// 49// Symbolic Evaluation of Chains of Recurrences for Loop Optimization 50// Robert A. van Engelen 51// 52// Efficient Symbolic Analysis for Optimizing Compilers 53// Robert A. van Engelen 54// 55// Using the chains of recurrences algebra for data dependence testing and 56// induction variable substitution 57// MS Thesis, Johnie Birch 58// 59//===----------------------------------------------------------------------===// 60 61#define DEBUG_TYPE "scalar-evolution" 62#include "llvm/Analysis/ScalarEvolutionExpressions.h" 63#include "llvm/Constants.h" 64#include "llvm/DerivedTypes.h" 65#include "llvm/GlobalVariable.h" 66#include "llvm/GlobalAlias.h" 67#include "llvm/Instructions.h" 68#include "llvm/LLVMContext.h" 69#include "llvm/Operator.h" 70#include "llvm/Analysis/ConstantFolding.h" 71#include "llvm/Analysis/Dominators.h" 72#include "llvm/Analysis/InstructionSimplify.h" 73#include "llvm/Analysis/LoopInfo.h" 74#include "llvm/Analysis/ValueTracking.h" 75#include "llvm/Assembly/Writer.h" 76#include "llvm/Target/TargetData.h" 77#include "llvm/Support/CommandLine.h" 78#include "llvm/Support/ConstantRange.h" 79#include "llvm/Support/Debug.h" 80#include "llvm/Support/ErrorHandling.h" 81#include "llvm/Support/GetElementPtrTypeIterator.h" 82#include "llvm/Support/InstIterator.h" 83#include "llvm/Support/MathExtras.h" 84#include "llvm/Support/raw_ostream.h" 85#include "llvm/ADT/Statistic.h" 86#include "llvm/ADT/STLExtras.h" 87#include "llvm/ADT/SmallPtrSet.h" 88#include <algorithm> 89using namespace llvm; 90 91STATISTIC(NumArrayLenItCounts, 92 "Number of trip counts computed with array length"); 93STATISTIC(NumTripCountsComputed, 94 "Number of loops with predictable loop counts"); 95STATISTIC(NumTripCountsNotComputed, 96 "Number of loops without predictable loop counts"); 97STATISTIC(NumBruteForceTripCountsComputed, 98 "Number of loops with trip counts computed by force"); 99 100static cl::opt<unsigned> 101MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden, 102 cl::desc("Maximum number of iterations SCEV will " 103 "symbolically execute a constant " 104 "derived loop"), 105 cl::init(100)); 106 107INITIALIZE_PASS_BEGIN(ScalarEvolution, "scalar-evolution", 108 "Scalar Evolution Analysis", false, true) 109INITIALIZE_PASS_DEPENDENCY(LoopInfo) 110INITIALIZE_PASS_DEPENDENCY(DominatorTree) 111INITIALIZE_PASS_END(ScalarEvolution, "scalar-evolution", 112 "Scalar Evolution Analysis", false, true) 113char ScalarEvolution::ID = 0; 114 115//===----------------------------------------------------------------------===// 116// SCEV class definitions 117//===----------------------------------------------------------------------===// 118 119//===----------------------------------------------------------------------===// 120// Implementation of the SCEV class. 121// 122 123void SCEV::dump() const { 124 print(dbgs()); 125 dbgs() << '\n'; 126} 127 128void SCEV::print(raw_ostream &OS) const { 129 switch (getSCEVType()) { 130 case scConstant: 131 WriteAsOperand(OS, cast<SCEVConstant>(this)->getValue(), false); 132 return; 133 case scTruncate: { 134 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this); 135 const SCEV *Op = Trunc->getOperand(); 136 OS << "(trunc " << *Op->getType() << " " << *Op << " to " 137 << *Trunc->getType() << ")"; 138 return; 139 } 140 case scZeroExtend: { 141 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this); 142 const SCEV *Op = ZExt->getOperand(); 143 OS << "(zext " << *Op->getType() << " " << *Op << " to " 144 << *ZExt->getType() << ")"; 145 return; 146 } 147 case scSignExtend: { 148 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this); 149 const SCEV *Op = SExt->getOperand(); 150 OS << "(sext " << *Op->getType() << " " << *Op << " to " 151 << *SExt->getType() << ")"; 152 return; 153 } 154 case scAddRecExpr: { 155 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this); 156 OS << "{" << *AR->getOperand(0); 157 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i) 158 OS << ",+," << *AR->getOperand(i); 159 OS << "}<"; 160 if (AR->getNoWrapFlags(FlagNUW)) 161 OS << "nuw><"; 162 if (AR->getNoWrapFlags(FlagNSW)) 163 OS << "nsw><"; 164 if (AR->getNoWrapFlags(FlagNW) && 165 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW))) 166 OS << "nw><"; 167 WriteAsOperand(OS, AR->getLoop()->getHeader(), /*PrintType=*/false); 168 OS << ">"; 169 return; 170 } 171 case scAddExpr: 172 case scMulExpr: 173 case scUMaxExpr: 174 case scSMaxExpr: { 175 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this); 176 const char *OpStr = 0; 177 switch (NAry->getSCEVType()) { 178 case scAddExpr: OpStr = " + "; break; 179 case scMulExpr: OpStr = " * "; break; 180 case scUMaxExpr: OpStr = " umax "; break; 181 case scSMaxExpr: OpStr = " smax "; break; 182 } 183 OS << "("; 184 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 185 I != E; ++I) { 186 OS << **I; 187 if (llvm::next(I) != E) 188 OS << OpStr; 189 } 190 OS << ")"; 191 return; 192 } 193 case scUDivExpr: { 194 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this); 195 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")"; 196 return; 197 } 198 case scUnknown: { 199 const SCEVUnknown *U = cast<SCEVUnknown>(this); 200 Type *AllocTy; 201 if (U->isSizeOf(AllocTy)) { 202 OS << "sizeof(" << *AllocTy << ")"; 203 return; 204 } 205 if (U->isAlignOf(AllocTy)) { 206 OS << "alignof(" << *AllocTy << ")"; 207 return; 208 } 209 210 Type *CTy; 211 Constant *FieldNo; 212 if (U->isOffsetOf(CTy, FieldNo)) { 213 OS << "offsetof(" << *CTy << ", "; 214 WriteAsOperand(OS, FieldNo, false); 215 OS << ")"; 216 return; 217 } 218 219 // Otherwise just print it normally. 220 WriteAsOperand(OS, U->getValue(), false); 221 return; 222 } 223 case scCouldNotCompute: 224 OS << "***COULDNOTCOMPUTE***"; 225 return; 226 default: break; 227 } 228 llvm_unreachable("Unknown SCEV kind!"); 229} 230 231Type *SCEV::getType() const { 232 switch (getSCEVType()) { 233 case scConstant: 234 return cast<SCEVConstant>(this)->getType(); 235 case scTruncate: 236 case scZeroExtend: 237 case scSignExtend: 238 return cast<SCEVCastExpr>(this)->getType(); 239 case scAddRecExpr: 240 case scMulExpr: 241 case scUMaxExpr: 242 case scSMaxExpr: 243 return cast<SCEVNAryExpr>(this)->getType(); 244 case scAddExpr: 245 return cast<SCEVAddExpr>(this)->getType(); 246 case scUDivExpr: 247 return cast<SCEVUDivExpr>(this)->getType(); 248 case scUnknown: 249 return cast<SCEVUnknown>(this)->getType(); 250 case scCouldNotCompute: 251 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 252 return 0; 253 default: break; 254 } 255 llvm_unreachable("Unknown SCEV kind!"); 256 return 0; 257} 258 259bool SCEV::isZero() const { 260 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 261 return SC->getValue()->isZero(); 262 return false; 263} 264 265bool SCEV::isOne() const { 266 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 267 return SC->getValue()->isOne(); 268 return false; 269} 270 271bool SCEV::isAllOnesValue() const { 272 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 273 return SC->getValue()->isAllOnesValue(); 274 return false; 275} 276 277SCEVCouldNotCompute::SCEVCouldNotCompute() : 278 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {} 279 280bool SCEVCouldNotCompute::classof(const SCEV *S) { 281 return S->getSCEVType() == scCouldNotCompute; 282} 283 284const SCEV *ScalarEvolution::getConstant(ConstantInt *V) { 285 FoldingSetNodeID ID; 286 ID.AddInteger(scConstant); 287 ID.AddPointer(V); 288 void *IP = 0; 289 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 290 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V); 291 UniqueSCEVs.InsertNode(S, IP); 292 return S; 293} 294 295const SCEV *ScalarEvolution::getConstant(const APInt& Val) { 296 return getConstant(ConstantInt::get(getContext(), Val)); 297} 298 299const SCEV * 300ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) { 301 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty)); 302 return getConstant(ConstantInt::get(ITy, V, isSigned)); 303} 304 305SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID, 306 unsigned SCEVTy, const SCEV *op, Type *ty) 307 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {} 308 309SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID, 310 const SCEV *op, Type *ty) 311 : SCEVCastExpr(ID, scTruncate, op, ty) { 312 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 313 (Ty->isIntegerTy() || Ty->isPointerTy()) && 314 "Cannot truncate non-integer value!"); 315} 316 317SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID, 318 const SCEV *op, Type *ty) 319 : SCEVCastExpr(ID, scZeroExtend, op, ty) { 320 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 321 (Ty->isIntegerTy() || Ty->isPointerTy()) && 322 "Cannot zero extend non-integer value!"); 323} 324 325SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID, 326 const SCEV *op, Type *ty) 327 : SCEVCastExpr(ID, scSignExtend, op, ty) { 328 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 329 (Ty->isIntegerTy() || Ty->isPointerTy()) && 330 "Cannot sign extend non-integer value!"); 331} 332 333void SCEVUnknown::deleted() { 334 // Clear this SCEVUnknown from various maps. 335 SE->forgetMemoizedResults(this); 336 337 // Remove this SCEVUnknown from the uniquing map. 338 SE->UniqueSCEVs.RemoveNode(this); 339 340 // Release the value. 341 setValPtr(0); 342} 343 344void SCEVUnknown::allUsesReplacedWith(Value *New) { 345 // Clear this SCEVUnknown from various maps. 346 SE->forgetMemoizedResults(this); 347 348 // Remove this SCEVUnknown from the uniquing map. 349 SE->UniqueSCEVs.RemoveNode(this); 350 351 // Update this SCEVUnknown to point to the new value. This is needed 352 // because there may still be outstanding SCEVs which still point to 353 // this SCEVUnknown. 354 setValPtr(New); 355} 356 357bool SCEVUnknown::isSizeOf(Type *&AllocTy) const { 358 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 359 if (VCE->getOpcode() == Instruction::PtrToInt) 360 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 361 if (CE->getOpcode() == Instruction::GetElementPtr && 362 CE->getOperand(0)->isNullValue() && 363 CE->getNumOperands() == 2) 364 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1))) 365 if (CI->isOne()) { 366 AllocTy = cast<PointerType>(CE->getOperand(0)->getType()) 367 ->getElementType(); 368 return true; 369 } 370 371 return false; 372} 373 374bool SCEVUnknown::isAlignOf(Type *&AllocTy) const { 375 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 376 if (VCE->getOpcode() == Instruction::PtrToInt) 377 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 378 if (CE->getOpcode() == Instruction::GetElementPtr && 379 CE->getOperand(0)->isNullValue()) { 380 Type *Ty = 381 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 382 if (StructType *STy = dyn_cast<StructType>(Ty)) 383 if (!STy->isPacked() && 384 CE->getNumOperands() == 3 && 385 CE->getOperand(1)->isNullValue()) { 386 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2))) 387 if (CI->isOne() && 388 STy->getNumElements() == 2 && 389 STy->getElementType(0)->isIntegerTy(1)) { 390 AllocTy = STy->getElementType(1); 391 return true; 392 } 393 } 394 } 395 396 return false; 397} 398 399bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const { 400 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 401 if (VCE->getOpcode() == Instruction::PtrToInt) 402 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 403 if (CE->getOpcode() == Instruction::GetElementPtr && 404 CE->getNumOperands() == 3 && 405 CE->getOperand(0)->isNullValue() && 406 CE->getOperand(1)->isNullValue()) { 407 Type *Ty = 408 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 409 // Ignore vector types here so that ScalarEvolutionExpander doesn't 410 // emit getelementptrs that index into vectors. 411 if (Ty->isStructTy() || Ty->isArrayTy()) { 412 CTy = Ty; 413 FieldNo = CE->getOperand(2); 414 return true; 415 } 416 } 417 418 return false; 419} 420 421//===----------------------------------------------------------------------===// 422// SCEV Utilities 423//===----------------------------------------------------------------------===// 424 425namespace { 426 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 427 /// than the complexity of the RHS. This comparator is used to canonicalize 428 /// expressions. 429 class SCEVComplexityCompare { 430 const LoopInfo *const LI; 431 public: 432 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {} 433 434 // Return true or false if LHS is less than, or at least RHS, respectively. 435 bool operator()(const SCEV *LHS, const SCEV *RHS) const { 436 return compare(LHS, RHS) < 0; 437 } 438 439 // Return negative, zero, or positive, if LHS is less than, equal to, or 440 // greater than RHS, respectively. A three-way result allows recursive 441 // comparisons to be more efficient. 442 int compare(const SCEV *LHS, const SCEV *RHS) const { 443 // Fast-path: SCEVs are uniqued so we can do a quick equality check. 444 if (LHS == RHS) 445 return 0; 446 447 // Primarily, sort the SCEVs by their getSCEVType(). 448 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType(); 449 if (LType != RType) 450 return (int)LType - (int)RType; 451 452 // Aside from the getSCEVType() ordering, the particular ordering 453 // isn't very important except that it's beneficial to be consistent, 454 // so that (a + b) and (b + a) don't end up as different expressions. 455 switch (LType) { 456 case scUnknown: { 457 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS); 458 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS); 459 460 // Sort SCEVUnknown values with some loose heuristics. TODO: This is 461 // not as complete as it could be. 462 const Value *LV = LU->getValue(), *RV = RU->getValue(); 463 464 // Order pointer values after integer values. This helps SCEVExpander 465 // form GEPs. 466 bool LIsPointer = LV->getType()->isPointerTy(), 467 RIsPointer = RV->getType()->isPointerTy(); 468 if (LIsPointer != RIsPointer) 469 return (int)LIsPointer - (int)RIsPointer; 470 471 // Compare getValueID values. 472 unsigned LID = LV->getValueID(), 473 RID = RV->getValueID(); 474 if (LID != RID) 475 return (int)LID - (int)RID; 476 477 // Sort arguments by their position. 478 if (const Argument *LA = dyn_cast<Argument>(LV)) { 479 const Argument *RA = cast<Argument>(RV); 480 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo(); 481 return (int)LArgNo - (int)RArgNo; 482 } 483 484 // For instructions, compare their loop depth, and their operand 485 // count. This is pretty loose. 486 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) { 487 const Instruction *RInst = cast<Instruction>(RV); 488 489 // Compare loop depths. 490 const BasicBlock *LParent = LInst->getParent(), 491 *RParent = RInst->getParent(); 492 if (LParent != RParent) { 493 unsigned LDepth = LI->getLoopDepth(LParent), 494 RDepth = LI->getLoopDepth(RParent); 495 if (LDepth != RDepth) 496 return (int)LDepth - (int)RDepth; 497 } 498 499 // Compare the number of operands. 500 unsigned LNumOps = LInst->getNumOperands(), 501 RNumOps = RInst->getNumOperands(); 502 return (int)LNumOps - (int)RNumOps; 503 } 504 505 return 0; 506 } 507 508 case scConstant: { 509 const SCEVConstant *LC = cast<SCEVConstant>(LHS); 510 const SCEVConstant *RC = cast<SCEVConstant>(RHS); 511 512 // Compare constant values. 513 const APInt &LA = LC->getValue()->getValue(); 514 const APInt &RA = RC->getValue()->getValue(); 515 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth(); 516 if (LBitWidth != RBitWidth) 517 return (int)LBitWidth - (int)RBitWidth; 518 return LA.ult(RA) ? -1 : 1; 519 } 520 521 case scAddRecExpr: { 522 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS); 523 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS); 524 525 // Compare addrec loop depths. 526 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop(); 527 if (LLoop != RLoop) { 528 unsigned LDepth = LLoop->getLoopDepth(), 529 RDepth = RLoop->getLoopDepth(); 530 if (LDepth != RDepth) 531 return (int)LDepth - (int)RDepth; 532 } 533 534 // Addrec complexity grows with operand count. 535 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands(); 536 if (LNumOps != RNumOps) 537 return (int)LNumOps - (int)RNumOps; 538 539 // Lexicographically compare. 540 for (unsigned i = 0; i != LNumOps; ++i) { 541 long X = compare(LA->getOperand(i), RA->getOperand(i)); 542 if (X != 0) 543 return X; 544 } 545 546 return 0; 547 } 548 549 case scAddExpr: 550 case scMulExpr: 551 case scSMaxExpr: 552 case scUMaxExpr: { 553 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS); 554 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS); 555 556 // Lexicographically compare n-ary expressions. 557 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands(); 558 for (unsigned i = 0; i != LNumOps; ++i) { 559 if (i >= RNumOps) 560 return 1; 561 long X = compare(LC->getOperand(i), RC->getOperand(i)); 562 if (X != 0) 563 return X; 564 } 565 return (int)LNumOps - (int)RNumOps; 566 } 567 568 case scUDivExpr: { 569 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS); 570 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS); 571 572 // Lexicographically compare udiv expressions. 573 long X = compare(LC->getLHS(), RC->getLHS()); 574 if (X != 0) 575 return X; 576 return compare(LC->getRHS(), RC->getRHS()); 577 } 578 579 case scTruncate: 580 case scZeroExtend: 581 case scSignExtend: { 582 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS); 583 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS); 584 585 // Compare cast expressions by operand. 586 return compare(LC->getOperand(), RC->getOperand()); 587 } 588 589 default: 590 break; 591 } 592 593 llvm_unreachable("Unknown SCEV kind!"); 594 return 0; 595 } 596 }; 597} 598 599/// GroupByComplexity - Given a list of SCEV objects, order them by their 600/// complexity, and group objects of the same complexity together by value. 601/// When this routine is finished, we know that any duplicates in the vector are 602/// consecutive and that complexity is monotonically increasing. 603/// 604/// Note that we go take special precautions to ensure that we get deterministic 605/// results from this routine. In other words, we don't want the results of 606/// this to depend on where the addresses of various SCEV objects happened to 607/// land in memory. 608/// 609static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops, 610 LoopInfo *LI) { 611 if (Ops.size() < 2) return; // Noop 612 if (Ops.size() == 2) { 613 // This is the common case, which also happens to be trivially simple. 614 // Special case it. 615 const SCEV *&LHS = Ops[0], *&RHS = Ops[1]; 616 if (SCEVComplexityCompare(LI)(RHS, LHS)) 617 std::swap(LHS, RHS); 618 return; 619 } 620 621 // Do the rough sort by complexity. 622 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI)); 623 624 // Now that we are sorted by complexity, group elements of the same 625 // complexity. Note that this is, at worst, N^2, but the vector is likely to 626 // be extremely short in practice. Note that we take this approach because we 627 // do not want to depend on the addresses of the objects we are grouping. 628 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 629 const SCEV *S = Ops[i]; 630 unsigned Complexity = S->getSCEVType(); 631 632 // If there are any objects of the same complexity and same value as this 633 // one, group them. 634 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 635 if (Ops[j] == S) { // Found a duplicate. 636 // Move it to immediately after i'th element. 637 std::swap(Ops[i+1], Ops[j]); 638 ++i; // no need to rescan it. 639 if (i == e-2) return; // Done! 640 } 641 } 642 } 643} 644 645 646 647//===----------------------------------------------------------------------===// 648// Simple SCEV method implementations 649//===----------------------------------------------------------------------===// 650 651/// BinomialCoefficient - Compute BC(It, K). The result has width W. 652/// Assume, K > 0. 653static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K, 654 ScalarEvolution &SE, 655 Type* ResultTy) { 656 // Handle the simplest case efficiently. 657 if (K == 1) 658 return SE.getTruncateOrZeroExtend(It, ResultTy); 659 660 // We are using the following formula for BC(It, K): 661 // 662 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 663 // 664 // Suppose, W is the bitwidth of the return value. We must be prepared for 665 // overflow. Hence, we must assure that the result of our computation is 666 // equal to the accurate one modulo 2^W. Unfortunately, division isn't 667 // safe in modular arithmetic. 668 // 669 // However, this code doesn't use exactly that formula; the formula it uses 670 // is something like the following, where T is the number of factors of 2 in 671 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is 672 // exponentiation: 673 // 674 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T) 675 // 676 // This formula is trivially equivalent to the previous formula. However, 677 // this formula can be implemented much more efficiently. The trick is that 678 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular 679 // arithmetic. To do exact division in modular arithmetic, all we have 680 // to do is multiply by the inverse. Therefore, this step can be done at 681 // width W. 682 // 683 // The next issue is how to safely do the division by 2^T. The way this 684 // is done is by doing the multiplication step at a width of at least W + T 685 // bits. This way, the bottom W+T bits of the product are accurate. Then, 686 // when we perform the division by 2^T (which is equivalent to a right shift 687 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get 688 // truncated out after the division by 2^T. 689 // 690 // In comparison to just directly using the first formula, this technique 691 // is much more efficient; using the first formula requires W * K bits, 692 // but this formula less than W + K bits. Also, the first formula requires 693 // a division step, whereas this formula only requires multiplies and shifts. 694 // 695 // It doesn't matter whether the subtraction step is done in the calculation 696 // width or the input iteration count's width; if the subtraction overflows, 697 // the result must be zero anyway. We prefer here to do it in the width of 698 // the induction variable because it helps a lot for certain cases; CodeGen 699 // isn't smart enough to ignore the overflow, which leads to much less 700 // efficient code if the width of the subtraction is wider than the native 701 // register width. 702 // 703 // (It's possible to not widen at all by pulling out factors of 2 before 704 // the multiplication; for example, K=2 can be calculated as 705 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires 706 // extra arithmetic, so it's not an obvious win, and it gets 707 // much more complicated for K > 3.) 708 709 // Protection from insane SCEVs; this bound is conservative, 710 // but it probably doesn't matter. 711 if (K > 1000) 712 return SE.getCouldNotCompute(); 713 714 unsigned W = SE.getTypeSizeInBits(ResultTy); 715 716 // Calculate K! / 2^T and T; we divide out the factors of two before 717 // multiplying for calculating K! / 2^T to avoid overflow. 718 // Other overflow doesn't matter because we only care about the bottom 719 // W bits of the result. 720 APInt OddFactorial(W, 1); 721 unsigned T = 1; 722 for (unsigned i = 3; i <= K; ++i) { 723 APInt Mult(W, i); 724 unsigned TwoFactors = Mult.countTrailingZeros(); 725 T += TwoFactors; 726 Mult = Mult.lshr(TwoFactors); 727 OddFactorial *= Mult; 728 } 729 730 // We need at least W + T bits for the multiplication step 731 unsigned CalculationBits = W + T; 732 733 // Calculate 2^T, at width T+W. 734 APInt DivFactor = APInt(CalculationBits, 1).shl(T); 735 736 // Calculate the multiplicative inverse of K! / 2^T; 737 // this multiplication factor will perform the exact division by 738 // K! / 2^T. 739 APInt Mod = APInt::getSignedMinValue(W+1); 740 APInt MultiplyFactor = OddFactorial.zext(W+1); 741 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod); 742 MultiplyFactor = MultiplyFactor.trunc(W); 743 744 // Calculate the product, at width T+W 745 IntegerType *CalculationTy = IntegerType::get(SE.getContext(), 746 CalculationBits); 747 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy); 748 for (unsigned i = 1; i != K; ++i) { 749 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i)); 750 Dividend = SE.getMulExpr(Dividend, 751 SE.getTruncateOrZeroExtend(S, CalculationTy)); 752 } 753 754 // Divide by 2^T 755 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor)); 756 757 // Truncate the result, and divide by K! / 2^T. 758 759 return SE.getMulExpr(SE.getConstant(MultiplyFactor), 760 SE.getTruncateOrZeroExtend(DivResult, ResultTy)); 761} 762 763/// evaluateAtIteration - Return the value of this chain of recurrences at 764/// the specified iteration number. We can evaluate this recurrence by 765/// multiplying each element in the chain by the binomial coefficient 766/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 767/// 768/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 769/// 770/// where BC(It, k) stands for binomial coefficient. 771/// 772const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It, 773 ScalarEvolution &SE) const { 774 const SCEV *Result = getStart(); 775 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 776 // The computation is correct in the face of overflow provided that the 777 // multiplication is performed _after_ the evaluation of the binomial 778 // coefficient. 779 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType()); 780 if (isa<SCEVCouldNotCompute>(Coeff)) 781 return Coeff; 782 783 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff)); 784 } 785 return Result; 786} 787 788//===----------------------------------------------------------------------===// 789// SCEV Expression folder implementations 790//===----------------------------------------------------------------------===// 791 792const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, 793 Type *Ty) { 794 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && 795 "This is not a truncating conversion!"); 796 assert(isSCEVable(Ty) && 797 "This is not a conversion to a SCEVable type!"); 798 Ty = getEffectiveSCEVType(Ty); 799 800 FoldingSetNodeID ID; 801 ID.AddInteger(scTruncate); 802 ID.AddPointer(Op); 803 ID.AddPointer(Ty); 804 void *IP = 0; 805 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 806 807 // Fold if the operand is constant. 808 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 809 return getConstant( 810 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), 811 getEffectiveSCEVType(Ty)))); 812 813 // trunc(trunc(x)) --> trunc(x) 814 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) 815 return getTruncateExpr(ST->getOperand(), Ty); 816 817 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing 818 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 819 return getTruncateOrSignExtend(SS->getOperand(), Ty); 820 821 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing 822 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 823 return getTruncateOrZeroExtend(SZ->getOperand(), Ty); 824 825 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can 826 // eliminate all the truncates. 827 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) { 828 SmallVector<const SCEV *, 4> Operands; 829 bool hasTrunc = false; 830 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) { 831 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty); 832 hasTrunc = isa<SCEVTruncateExpr>(S); 833 Operands.push_back(S); 834 } 835 if (!hasTrunc) 836 return getAddExpr(Operands); 837 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL. 838 } 839 840 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can 841 // eliminate all the truncates. 842 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) { 843 SmallVector<const SCEV *, 4> Operands; 844 bool hasTrunc = false; 845 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) { 846 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty); 847 hasTrunc = isa<SCEVTruncateExpr>(S); 848 Operands.push_back(S); 849 } 850 if (!hasTrunc) 851 return getMulExpr(Operands); 852 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL. 853 } 854 855 // If the input value is a chrec scev, truncate the chrec's operands. 856 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 857 SmallVector<const SCEV *, 4> Operands; 858 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 859 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 860 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap); 861 } 862 863 // As a special case, fold trunc(undef) to undef. We don't want to 864 // know too much about SCEVUnknowns, but this special case is handy 865 // and harmless. 866 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op)) 867 if (isa<UndefValue>(U->getValue())) 868 return getSCEV(UndefValue::get(Ty)); 869 870 // The cast wasn't folded; create an explicit cast node. We can reuse 871 // the existing insert position since if we get here, we won't have 872 // made any changes which would invalidate it. 873 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator), 874 Op, Ty); 875 UniqueSCEVs.InsertNode(S, IP); 876 return S; 877} 878 879const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op, 880 Type *Ty) { 881 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 882 "This is not an extending conversion!"); 883 assert(isSCEVable(Ty) && 884 "This is not a conversion to a SCEVable type!"); 885 Ty = getEffectiveSCEVType(Ty); 886 887 // Fold if the operand is constant. 888 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 889 return getConstant( 890 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), 891 getEffectiveSCEVType(Ty)))); 892 893 // zext(zext(x)) --> zext(x) 894 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 895 return getZeroExtendExpr(SZ->getOperand(), Ty); 896 897 // Before doing any expensive analysis, check to see if we've already 898 // computed a SCEV for this Op and Ty. 899 FoldingSetNodeID ID; 900 ID.AddInteger(scZeroExtend); 901 ID.AddPointer(Op); 902 ID.AddPointer(Ty); 903 void *IP = 0; 904 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 905 906 // zext(trunc(x)) --> zext(x) or x or trunc(x) 907 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) { 908 // It's possible the bits taken off by the truncate were all zero bits. If 909 // so, we should be able to simplify this further. 910 const SCEV *X = ST->getOperand(); 911 ConstantRange CR = getUnsignedRange(X); 912 unsigned TruncBits = getTypeSizeInBits(ST->getType()); 913 unsigned NewBits = getTypeSizeInBits(Ty); 914 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains( 915 CR.zextOrTrunc(NewBits))) 916 return getTruncateOrZeroExtend(X, Ty); 917 } 918 919 // If the input value is a chrec scev, and we can prove that the value 920 // did not overflow the old, smaller, value, we can zero extend all of the 921 // operands (often constants). This allows analysis of something like 922 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 923 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 924 if (AR->isAffine()) { 925 const SCEV *Start = AR->getStart(); 926 const SCEV *Step = AR->getStepRecurrence(*this); 927 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 928 const Loop *L = AR->getLoop(); 929 930 // If we have special knowledge that this addrec won't overflow, 931 // we don't need to do any further analysis. 932 if (AR->getNoWrapFlags(SCEV::FlagNUW)) 933 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 934 getZeroExtendExpr(Step, Ty), 935 L, AR->getNoWrapFlags()); 936 937 // Check whether the backedge-taken count is SCEVCouldNotCompute. 938 // Note that this serves two purposes: It filters out loops that are 939 // simply not analyzable, and it covers the case where this code is 940 // being called from within backedge-taken count analysis, such that 941 // attempting to ask for the backedge-taken count would likely result 942 // in infinite recursion. In the later case, the analysis code will 943 // cope with a conservative value, and it will take care to purge 944 // that value once it has finished. 945 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 946 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 947 // Manually compute the final value for AR, checking for 948 // overflow. 949 950 // Check whether the backedge-taken count can be losslessly casted to 951 // the addrec's type. The count is always unsigned. 952 const SCEV *CastedMaxBECount = 953 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 954 const SCEV *RecastedMaxBECount = 955 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 956 if (MaxBECount == RecastedMaxBECount) { 957 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 958 // Check whether Start+Step*MaxBECount has no unsigned overflow. 959 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step); 960 const SCEV *Add = getAddExpr(Start, ZMul); 961 const SCEV *OperandExtendedAdd = 962 getAddExpr(getZeroExtendExpr(Start, WideTy), 963 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 964 getZeroExtendExpr(Step, WideTy))); 965 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) { 966 // Cache knowledge of AR NUW, which is propagated to this AddRec. 967 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW); 968 // Return the expression with the addrec on the outside. 969 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 970 getZeroExtendExpr(Step, Ty), 971 L, AR->getNoWrapFlags()); 972 } 973 // Similar to above, only this time treat the step value as signed. 974 // This covers loops that count down. 975 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); 976 Add = getAddExpr(Start, SMul); 977 OperandExtendedAdd = 978 getAddExpr(getZeroExtendExpr(Start, WideTy), 979 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 980 getSignExtendExpr(Step, WideTy))); 981 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) { 982 // Cache knowledge of AR NW, which is propagated to this AddRec. 983 // Negative step causes unsigned wrap, but it still can't self-wrap. 984 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW); 985 // Return the expression with the addrec on the outside. 986 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 987 getSignExtendExpr(Step, Ty), 988 L, AR->getNoWrapFlags()); 989 } 990 } 991 992 // If the backedge is guarded by a comparison with the pre-inc value 993 // the addrec is safe. Also, if the entry is guarded by a comparison 994 // with the start value and the backedge is guarded by a comparison 995 // with the post-inc value, the addrec is safe. 996 if (isKnownPositive(Step)) { 997 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) - 998 getUnsignedRange(Step).getUnsignedMax()); 999 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) || 1000 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) && 1001 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, 1002 AR->getPostIncExpr(*this), N))) { 1003 // Cache knowledge of AR NUW, which is propagated to this AddRec. 1004 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW); 1005 // Return the expression with the addrec on the outside. 1006 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 1007 getZeroExtendExpr(Step, Ty), 1008 L, AR->getNoWrapFlags()); 1009 } 1010 } else if (isKnownNegative(Step)) { 1011 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) - 1012 getSignedRange(Step).getSignedMin()); 1013 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) || 1014 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) && 1015 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, 1016 AR->getPostIncExpr(*this), N))) { 1017 // Cache knowledge of AR NW, which is propagated to this AddRec. 1018 // Negative step causes unsigned wrap, but it still can't self-wrap. 1019 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW); 1020 // Return the expression with the addrec on the outside. 1021 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 1022 getSignExtendExpr(Step, Ty), 1023 L, AR->getNoWrapFlags()); 1024 } 1025 } 1026 } 1027 } 1028 1029 // The cast wasn't folded; create an explicit cast node. 1030 // Recompute the insert position, as it may have been invalidated. 1031 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1032 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator), 1033 Op, Ty); 1034 UniqueSCEVs.InsertNode(S, IP); 1035 return S; 1036} 1037 1038// Get the limit of a recurrence such that incrementing by Step cannot cause 1039// signed overflow as long as the value of the recurrence within the loop does 1040// not exceed this limit before incrementing. 1041static const SCEV *getOverflowLimitForStep(const SCEV *Step, 1042 ICmpInst::Predicate *Pred, 1043 ScalarEvolution *SE) { 1044 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType()); 1045 if (SE->isKnownPositive(Step)) { 1046 *Pred = ICmpInst::ICMP_SLT; 1047 return SE->getConstant(APInt::getSignedMinValue(BitWidth) - 1048 SE->getSignedRange(Step).getSignedMax()); 1049 } 1050 if (SE->isKnownNegative(Step)) { 1051 *Pred = ICmpInst::ICMP_SGT; 1052 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) - 1053 SE->getSignedRange(Step).getSignedMin()); 1054 } 1055 return 0; 1056} 1057 1058// The recurrence AR has been shown to have no signed wrap. Typically, if we can 1059// prove NSW for AR, then we can just as easily prove NSW for its preincrement 1060// or postincrement sibling. This allows normalizing a sign extended AddRec as 1061// such: {sext(Step + Start),+,Step} => {(Step + sext(Start),+,Step} As a 1062// result, the expression "Step + sext(PreIncAR)" is congruent with 1063// "sext(PostIncAR)" 1064static const SCEV *getPreStartForSignExtend(const SCEVAddRecExpr *AR, 1065 Type *Ty, 1066 ScalarEvolution *SE) { 1067 const Loop *L = AR->getLoop(); 1068 const SCEV *Start = AR->getStart(); 1069 const SCEV *Step = AR->getStepRecurrence(*SE); 1070 1071 // Check for a simple looking step prior to loop entry. 1072 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start); 1073 if (!SA || SA->getNumOperands() != 2 || SA->getOperand(0) != Step) 1074 return 0; 1075 1076 // This is a postinc AR. Check for overflow on the preinc recurrence using the 1077 // same three conditions that getSignExtendedExpr checks. 1078 1079 // 1. NSW flags on the step increment. 1080 const SCEV *PreStart = SA->getOperand(1); 1081 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>( 1082 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap)); 1083 1084 if (PreAR && PreAR->getNoWrapFlags(SCEV::FlagNSW)) 1085 return PreStart; 1086 1087 // 2. Direct overflow check on the step operation's expression. 1088 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType()); 1089 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2); 1090 const SCEV *OperandExtendedStart = 1091 SE->getAddExpr(SE->getSignExtendExpr(PreStart, WideTy), 1092 SE->getSignExtendExpr(Step, WideTy)); 1093 if (SE->getSignExtendExpr(Start, WideTy) == OperandExtendedStart) { 1094 // Cache knowledge of PreAR NSW. 1095 if (PreAR) 1096 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(SCEV::FlagNSW); 1097 // FIXME: this optimization needs a unit test 1098 DEBUG(dbgs() << "SCEV: untested prestart overflow check\n"); 1099 return PreStart; 1100 } 1101 1102 // 3. Loop precondition. 1103 ICmpInst::Predicate Pred; 1104 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, SE); 1105 1106 if (OverflowLimit && 1107 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) { 1108 return PreStart; 1109 } 1110 return 0; 1111} 1112 1113// Get the normalized sign-extended expression for this AddRec's Start. 1114static const SCEV *getSignExtendAddRecStart(const SCEVAddRecExpr *AR, 1115 Type *Ty, 1116 ScalarEvolution *SE) { 1117 const SCEV *PreStart = getPreStartForSignExtend(AR, Ty, SE); 1118 if (!PreStart) 1119 return SE->getSignExtendExpr(AR->getStart(), Ty); 1120 1121 return SE->getAddExpr(SE->getSignExtendExpr(AR->getStepRecurrence(*SE), Ty), 1122 SE->getSignExtendExpr(PreStart, Ty)); 1123} 1124 1125const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op, 1126 Type *Ty) { 1127 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1128 "This is not an extending conversion!"); 1129 assert(isSCEVable(Ty) && 1130 "This is not a conversion to a SCEVable type!"); 1131 Ty = getEffectiveSCEVType(Ty); 1132 1133 // Fold if the operand is constant. 1134 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1135 return getConstant( 1136 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), 1137 getEffectiveSCEVType(Ty)))); 1138 1139 // sext(sext(x)) --> sext(x) 1140 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 1141 return getSignExtendExpr(SS->getOperand(), Ty); 1142 1143 // sext(zext(x)) --> zext(x) 1144 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 1145 return getZeroExtendExpr(SZ->getOperand(), Ty); 1146 1147 // Before doing any expensive analysis, check to see if we've already 1148 // computed a SCEV for this Op and Ty. 1149 FoldingSetNodeID ID; 1150 ID.AddInteger(scSignExtend); 1151 ID.AddPointer(Op); 1152 ID.AddPointer(Ty); 1153 void *IP = 0; 1154 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1155 1156 // If the input value is provably positive, build a zext instead. 1157 if (isKnownNonNegative(Op)) 1158 return getZeroExtendExpr(Op, Ty); 1159 1160 // sext(trunc(x)) --> sext(x) or x or trunc(x) 1161 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) { 1162 // It's possible the bits taken off by the truncate were all sign bits. If 1163 // so, we should be able to simplify this further. 1164 const SCEV *X = ST->getOperand(); 1165 ConstantRange CR = getSignedRange(X); 1166 unsigned TruncBits = getTypeSizeInBits(ST->getType()); 1167 unsigned NewBits = getTypeSizeInBits(Ty); 1168 if (CR.truncate(TruncBits).signExtend(NewBits).contains( 1169 CR.sextOrTrunc(NewBits))) 1170 return getTruncateOrSignExtend(X, Ty); 1171 } 1172 1173 // If the input value is a chrec scev, and we can prove that the value 1174 // did not overflow the old, smaller, value, we can sign extend all of the 1175 // operands (often constants). This allows analysis of something like 1176 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 1177 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 1178 if (AR->isAffine()) { 1179 const SCEV *Start = AR->getStart(); 1180 const SCEV *Step = AR->getStepRecurrence(*this); 1181 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 1182 const Loop *L = AR->getLoop(); 1183 1184 // If we have special knowledge that this addrec won't overflow, 1185 // we don't need to do any further analysis. 1186 if (AR->getNoWrapFlags(SCEV::FlagNSW)) 1187 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this), 1188 getSignExtendExpr(Step, Ty), 1189 L, SCEV::FlagNSW); 1190 1191 // Check whether the backedge-taken count is SCEVCouldNotCompute. 1192 // Note that this serves two purposes: It filters out loops that are 1193 // simply not analyzable, and it covers the case where this code is 1194 // being called from within backedge-taken count analysis, such that 1195 // attempting to ask for the backedge-taken count would likely result 1196 // in infinite recursion. In the later case, the analysis code will 1197 // cope with a conservative value, and it will take care to purge 1198 // that value once it has finished. 1199 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 1200 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 1201 // Manually compute the final value for AR, checking for 1202 // overflow. 1203 1204 // Check whether the backedge-taken count can be losslessly casted to 1205 // the addrec's type. The count is always unsigned. 1206 const SCEV *CastedMaxBECount = 1207 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 1208 const SCEV *RecastedMaxBECount = 1209 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 1210 if (MaxBECount == RecastedMaxBECount) { 1211 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 1212 // Check whether Start+Step*MaxBECount has no signed overflow. 1213 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); 1214 const SCEV *Add = getAddExpr(Start, SMul); 1215 const SCEV *OperandExtendedAdd = 1216 getAddExpr(getSignExtendExpr(Start, WideTy), 1217 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1218 getSignExtendExpr(Step, WideTy))); 1219 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) { 1220 // Cache knowledge of AR NSW, which is propagated to this AddRec. 1221 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW); 1222 // Return the expression with the addrec on the outside. 1223 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this), 1224 getSignExtendExpr(Step, Ty), 1225 L, AR->getNoWrapFlags()); 1226 } 1227 // Similar to above, only this time treat the step value as unsigned. 1228 // This covers loops that count up with an unsigned step. 1229 const SCEV *UMul = getMulExpr(CastedMaxBECount, Step); 1230 Add = getAddExpr(Start, UMul); 1231 OperandExtendedAdd = 1232 getAddExpr(getSignExtendExpr(Start, WideTy), 1233 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1234 getZeroExtendExpr(Step, WideTy))); 1235 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) { 1236 // Cache knowledge of AR NSW, which is propagated to this AddRec. 1237 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW); 1238 // Return the expression with the addrec on the outside. 1239 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this), 1240 getZeroExtendExpr(Step, Ty), 1241 L, AR->getNoWrapFlags()); 1242 } 1243 } 1244 1245 // If the backedge is guarded by a comparison with the pre-inc value 1246 // the addrec is safe. Also, if the entry is guarded by a comparison 1247 // with the start value and the backedge is guarded by a comparison 1248 // with the post-inc value, the addrec is safe. 1249 ICmpInst::Predicate Pred; 1250 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, this); 1251 if (OverflowLimit && 1252 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) || 1253 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) && 1254 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this), 1255 OverflowLimit)))) { 1256 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec. 1257 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW); 1258 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this), 1259 getSignExtendExpr(Step, Ty), 1260 L, AR->getNoWrapFlags()); 1261 } 1262 } 1263 } 1264 1265 // The cast wasn't folded; create an explicit cast node. 1266 // Recompute the insert position, as it may have been invalidated. 1267 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1268 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator), 1269 Op, Ty); 1270 UniqueSCEVs.InsertNode(S, IP); 1271 return S; 1272} 1273 1274/// getAnyExtendExpr - Return a SCEV for the given operand extended with 1275/// unspecified bits out to the given type. 1276/// 1277const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op, 1278 Type *Ty) { 1279 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1280 "This is not an extending conversion!"); 1281 assert(isSCEVable(Ty) && 1282 "This is not a conversion to a SCEVable type!"); 1283 Ty = getEffectiveSCEVType(Ty); 1284 1285 // Sign-extend negative constants. 1286 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1287 if (SC->getValue()->getValue().isNegative()) 1288 return getSignExtendExpr(Op, Ty); 1289 1290 // Peel off a truncate cast. 1291 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) { 1292 const SCEV *NewOp = T->getOperand(); 1293 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty)) 1294 return getAnyExtendExpr(NewOp, Ty); 1295 return getTruncateOrNoop(NewOp, Ty); 1296 } 1297 1298 // Next try a zext cast. If the cast is folded, use it. 1299 const SCEV *ZExt = getZeroExtendExpr(Op, Ty); 1300 if (!isa<SCEVZeroExtendExpr>(ZExt)) 1301 return ZExt; 1302 1303 // Next try a sext cast. If the cast is folded, use it. 1304 const SCEV *SExt = getSignExtendExpr(Op, Ty); 1305 if (!isa<SCEVSignExtendExpr>(SExt)) 1306 return SExt; 1307 1308 // Force the cast to be folded into the operands of an addrec. 1309 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) { 1310 SmallVector<const SCEV *, 4> Ops; 1311 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end(); 1312 I != E; ++I) 1313 Ops.push_back(getAnyExtendExpr(*I, Ty)); 1314 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW); 1315 } 1316 1317 // As a special case, fold anyext(undef) to undef. We don't want to 1318 // know too much about SCEVUnknowns, but this special case is handy 1319 // and harmless. 1320 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op)) 1321 if (isa<UndefValue>(U->getValue())) 1322 return getSCEV(UndefValue::get(Ty)); 1323 1324 // If the expression is obviously signed, use the sext cast value. 1325 if (isa<SCEVSMaxExpr>(Op)) 1326 return SExt; 1327 1328 // Absent any other information, use the zext cast value. 1329 return ZExt; 1330} 1331 1332/// CollectAddOperandsWithScales - Process the given Ops list, which is 1333/// a list of operands to be added under the given scale, update the given 1334/// map. This is a helper function for getAddRecExpr. As an example of 1335/// what it does, given a sequence of operands that would form an add 1336/// expression like this: 1337/// 1338/// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r) 1339/// 1340/// where A and B are constants, update the map with these values: 1341/// 1342/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0) 1343/// 1344/// and add 13 + A*B*29 to AccumulatedConstant. 1345/// This will allow getAddRecExpr to produce this: 1346/// 1347/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B) 1348/// 1349/// This form often exposes folding opportunities that are hidden in 1350/// the original operand list. 1351/// 1352/// Return true iff it appears that any interesting folding opportunities 1353/// may be exposed. This helps getAddRecExpr short-circuit extra work in 1354/// the common case where no interesting opportunities are present, and 1355/// is also used as a check to avoid infinite recursion. 1356/// 1357static bool 1358CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M, 1359 SmallVector<const SCEV *, 8> &NewOps, 1360 APInt &AccumulatedConstant, 1361 const SCEV *const *Ops, size_t NumOperands, 1362 const APInt &Scale, 1363 ScalarEvolution &SE) { 1364 bool Interesting = false; 1365 1366 // Iterate over the add operands. They are sorted, with constants first. 1367 unsigned i = 0; 1368 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1369 ++i; 1370 // Pull a buried constant out to the outside. 1371 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero()) 1372 Interesting = true; 1373 AccumulatedConstant += Scale * C->getValue()->getValue(); 1374 } 1375 1376 // Next comes everything else. We're especially interested in multiplies 1377 // here, but they're in the middle, so just visit the rest with one loop. 1378 for (; i != NumOperands; ++i) { 1379 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]); 1380 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) { 1381 APInt NewScale = 1382 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue(); 1383 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) { 1384 // A multiplication of a constant with another add; recurse. 1385 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1)); 1386 Interesting |= 1387 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1388 Add->op_begin(), Add->getNumOperands(), 1389 NewScale, SE); 1390 } else { 1391 // A multiplication of a constant with some other value. Update 1392 // the map. 1393 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end()); 1394 const SCEV *Key = SE.getMulExpr(MulOps); 1395 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1396 M.insert(std::make_pair(Key, NewScale)); 1397 if (Pair.second) { 1398 NewOps.push_back(Pair.first->first); 1399 } else { 1400 Pair.first->second += NewScale; 1401 // The map already had an entry for this value, which may indicate 1402 // a folding opportunity. 1403 Interesting = true; 1404 } 1405 } 1406 } else { 1407 // An ordinary operand. Update the map. 1408 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1409 M.insert(std::make_pair(Ops[i], Scale)); 1410 if (Pair.second) { 1411 NewOps.push_back(Pair.first->first); 1412 } else { 1413 Pair.first->second += Scale; 1414 // The map already had an entry for this value, which may indicate 1415 // a folding opportunity. 1416 Interesting = true; 1417 } 1418 } 1419 } 1420 1421 return Interesting; 1422} 1423 1424namespace { 1425 struct APIntCompare { 1426 bool operator()(const APInt &LHS, const APInt &RHS) const { 1427 return LHS.ult(RHS); 1428 } 1429 }; 1430} 1431 1432/// getAddExpr - Get a canonical add expression, or something simpler if 1433/// possible. 1434const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops, 1435 SCEV::NoWrapFlags Flags) { 1436 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) && 1437 "only nuw or nsw allowed"); 1438 assert(!Ops.empty() && "Cannot get empty add!"); 1439 if (Ops.size() == 1) return Ops[0]; 1440#ifndef NDEBUG 1441 Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 1442 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1443 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 1444 "SCEVAddExpr operand types don't match!"); 1445#endif 1446 1447 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW. 1448 // And vice-versa. 1449 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW; 1450 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask); 1451 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) { 1452 bool All = true; 1453 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(), 1454 E = Ops.end(); I != E; ++I) 1455 if (!isKnownNonNegative(*I)) { 1456 All = false; 1457 break; 1458 } 1459 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask); 1460 } 1461 1462 // Sort by complexity, this groups all similar expression types together. 1463 GroupByComplexity(Ops, LI); 1464 1465 // If there are any constants, fold them together. 1466 unsigned Idx = 0; 1467 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1468 ++Idx; 1469 assert(Idx < Ops.size()); 1470 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1471 // We found two constants, fold them together! 1472 Ops[0] = getConstant(LHSC->getValue()->getValue() + 1473 RHSC->getValue()->getValue()); 1474 if (Ops.size() == 2) return Ops[0]; 1475 Ops.erase(Ops.begin()+1); // Erase the folded element 1476 LHSC = cast<SCEVConstant>(Ops[0]); 1477 } 1478 1479 // If we are left with a constant zero being added, strip it off. 1480 if (LHSC->getValue()->isZero()) { 1481 Ops.erase(Ops.begin()); 1482 --Idx; 1483 } 1484 1485 if (Ops.size() == 1) return Ops[0]; 1486 } 1487 1488 // Okay, check to see if the same value occurs in the operand list more than 1489 // once. If so, merge them together into an multiply expression. Since we 1490 // sorted the list, these values are required to be adjacent. 1491 Type *Ty = Ops[0]->getType(); 1492 bool FoundMatch = false; 1493 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i) 1494 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 1495 // Scan ahead to count how many equal operands there are. 1496 unsigned Count = 2; 1497 while (i+Count != e && Ops[i+Count] == Ops[i]) 1498 ++Count; 1499 // Merge the values into a multiply. 1500 const SCEV *Scale = getConstant(Ty, Count); 1501 const SCEV *Mul = getMulExpr(Scale, Ops[i]); 1502 if (Ops.size() == Count) 1503 return Mul; 1504 Ops[i] = Mul; 1505 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count); 1506 --i; e -= Count - 1; 1507 FoundMatch = true; 1508 } 1509 if (FoundMatch) 1510 return getAddExpr(Ops, Flags); 1511 1512 // Check for truncates. If all the operands are truncated from the same 1513 // type, see if factoring out the truncate would permit the result to be 1514 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n) 1515 // if the contents of the resulting outer trunc fold to something simple. 1516 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) { 1517 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]); 1518 Type *DstType = Trunc->getType(); 1519 Type *SrcType = Trunc->getOperand()->getType(); 1520 SmallVector<const SCEV *, 8> LargeOps; 1521 bool Ok = true; 1522 // Check all the operands to see if they can be represented in the 1523 // source type of the truncate. 1524 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1525 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) { 1526 if (T->getOperand()->getType() != SrcType) { 1527 Ok = false; 1528 break; 1529 } 1530 LargeOps.push_back(T->getOperand()); 1531 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1532 LargeOps.push_back(getAnyExtendExpr(C, SrcType)); 1533 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) { 1534 SmallVector<const SCEV *, 8> LargeMulOps; 1535 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) { 1536 if (const SCEVTruncateExpr *T = 1537 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) { 1538 if (T->getOperand()->getType() != SrcType) { 1539 Ok = false; 1540 break; 1541 } 1542 LargeMulOps.push_back(T->getOperand()); 1543 } else if (const SCEVConstant *C = 1544 dyn_cast<SCEVConstant>(M->getOperand(j))) { 1545 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType)); 1546 } else { 1547 Ok = false; 1548 break; 1549 } 1550 } 1551 if (Ok) 1552 LargeOps.push_back(getMulExpr(LargeMulOps)); 1553 } else { 1554 Ok = false; 1555 break; 1556 } 1557 } 1558 if (Ok) { 1559 // Evaluate the expression in the larger type. 1560 const SCEV *Fold = getAddExpr(LargeOps, Flags); 1561 // If it folds to something simple, use it. Otherwise, don't. 1562 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold)) 1563 return getTruncateExpr(Fold, DstType); 1564 } 1565 } 1566 1567 // Skip past any other cast SCEVs. 1568 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 1569 ++Idx; 1570 1571 // If there are add operands they would be next. 1572 if (Idx < Ops.size()) { 1573 bool DeletedAdd = false; 1574 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 1575 // If we have an add, expand the add operands onto the end of the operands 1576 // list. 1577 Ops.erase(Ops.begin()+Idx); 1578 Ops.append(Add->op_begin(), Add->op_end()); 1579 DeletedAdd = true; 1580 } 1581 1582 // If we deleted at least one add, we added operands to the end of the list, 1583 // and they are not necessarily sorted. Recurse to resort and resimplify 1584 // any operands we just acquired. 1585 if (DeletedAdd) 1586 return getAddExpr(Ops); 1587 } 1588 1589 // Skip over the add expression until we get to a multiply. 1590 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1591 ++Idx; 1592 1593 // Check to see if there are any folding opportunities present with 1594 // operands multiplied by constant values. 1595 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) { 1596 uint64_t BitWidth = getTypeSizeInBits(Ty); 1597 DenseMap<const SCEV *, APInt> M; 1598 SmallVector<const SCEV *, 8> NewOps; 1599 APInt AccumulatedConstant(BitWidth, 0); 1600 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1601 Ops.data(), Ops.size(), 1602 APInt(BitWidth, 1), *this)) { 1603 // Some interesting folding opportunity is present, so its worthwhile to 1604 // re-generate the operands list. Group the operands by constant scale, 1605 // to avoid multiplying by the same constant scale multiple times. 1606 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists; 1607 for (SmallVector<const SCEV *, 8>::const_iterator I = NewOps.begin(), 1608 E = NewOps.end(); I != E; ++I) 1609 MulOpLists[M.find(*I)->second].push_back(*I); 1610 // Re-generate the operands list. 1611 Ops.clear(); 1612 if (AccumulatedConstant != 0) 1613 Ops.push_back(getConstant(AccumulatedConstant)); 1614 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator 1615 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I) 1616 if (I->first != 0) 1617 Ops.push_back(getMulExpr(getConstant(I->first), 1618 getAddExpr(I->second))); 1619 if (Ops.empty()) 1620 return getConstant(Ty, 0); 1621 if (Ops.size() == 1) 1622 return Ops[0]; 1623 return getAddExpr(Ops); 1624 } 1625 } 1626 1627 // If we are adding something to a multiply expression, make sure the 1628 // something is not already an operand of the multiply. If so, merge it into 1629 // the multiply. 1630 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 1631 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 1632 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 1633 const SCEV *MulOpSCEV = Mul->getOperand(MulOp); 1634 if (isa<SCEVConstant>(MulOpSCEV)) 1635 continue; 1636 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 1637 if (MulOpSCEV == Ops[AddOp]) { 1638 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 1639 const SCEV *InnerMul = Mul->getOperand(MulOp == 0); 1640 if (Mul->getNumOperands() != 2) { 1641 // If the multiply has more than two operands, we must get the 1642 // Y*Z term. 1643 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1644 Mul->op_begin()+MulOp); 1645 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end()); 1646 InnerMul = getMulExpr(MulOps); 1647 } 1648 const SCEV *One = getConstant(Ty, 1); 1649 const SCEV *AddOne = getAddExpr(One, InnerMul); 1650 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV); 1651 if (Ops.size() == 2) return OuterMul; 1652 if (AddOp < Idx) { 1653 Ops.erase(Ops.begin()+AddOp); 1654 Ops.erase(Ops.begin()+Idx-1); 1655 } else { 1656 Ops.erase(Ops.begin()+Idx); 1657 Ops.erase(Ops.begin()+AddOp-1); 1658 } 1659 Ops.push_back(OuterMul); 1660 return getAddExpr(Ops); 1661 } 1662 1663 // Check this multiply against other multiplies being added together. 1664 for (unsigned OtherMulIdx = Idx+1; 1665 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 1666 ++OtherMulIdx) { 1667 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 1668 // If MulOp occurs in OtherMul, we can fold the two multiplies 1669 // together. 1670 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 1671 OMulOp != e; ++OMulOp) 1672 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 1673 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 1674 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0); 1675 if (Mul->getNumOperands() != 2) { 1676 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1677 Mul->op_begin()+MulOp); 1678 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end()); 1679 InnerMul1 = getMulExpr(MulOps); 1680 } 1681 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0); 1682 if (OtherMul->getNumOperands() != 2) { 1683 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(), 1684 OtherMul->op_begin()+OMulOp); 1685 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end()); 1686 InnerMul2 = getMulExpr(MulOps); 1687 } 1688 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 1689 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 1690 if (Ops.size() == 2) return OuterMul; 1691 Ops.erase(Ops.begin()+Idx); 1692 Ops.erase(Ops.begin()+OtherMulIdx-1); 1693 Ops.push_back(OuterMul); 1694 return getAddExpr(Ops); 1695 } 1696 } 1697 } 1698 } 1699 1700 // If there are any add recurrences in the operands list, see if any other 1701 // added values are loop invariant. If so, we can fold them into the 1702 // recurrence. 1703 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1704 ++Idx; 1705 1706 // Scan over all recurrences, trying to fold loop invariants into them. 1707 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1708 // Scan all of the other operands to this add and add them to the vector if 1709 // they are loop invariant w.r.t. the recurrence. 1710 SmallVector<const SCEV *, 8> LIOps; 1711 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1712 const Loop *AddRecLoop = AddRec->getLoop(); 1713 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1714 if (isLoopInvariant(Ops[i], AddRecLoop)) { 1715 LIOps.push_back(Ops[i]); 1716 Ops.erase(Ops.begin()+i); 1717 --i; --e; 1718 } 1719 1720 // If we found some loop invariants, fold them into the recurrence. 1721 if (!LIOps.empty()) { 1722 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 1723 LIOps.push_back(AddRec->getStart()); 1724 1725 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1726 AddRec->op_end()); 1727 AddRecOps[0] = getAddExpr(LIOps); 1728 1729 // Build the new addrec. Propagate the NUW and NSW flags if both the 1730 // outer add and the inner addrec are guaranteed to have no overflow. 1731 // Always propagate NW. 1732 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW)); 1733 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags); 1734 1735 // If all of the other operands were loop invariant, we are done. 1736 if (Ops.size() == 1) return NewRec; 1737 1738 // Otherwise, add the folded AddRec by the non-liv parts. 1739 for (unsigned i = 0;; ++i) 1740 if (Ops[i] == AddRec) { 1741 Ops[i] = NewRec; 1742 break; 1743 } 1744 return getAddExpr(Ops); 1745 } 1746 1747 // Okay, if there weren't any loop invariants to be folded, check to see if 1748 // there are multiple AddRec's with the same loop induction variable being 1749 // added together. If so, we can fold them. 1750 for (unsigned OtherIdx = Idx+1; 1751 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1752 ++OtherIdx) 1753 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) { 1754 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L> 1755 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1756 AddRec->op_end()); 1757 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1758 ++OtherIdx) 1759 if (const SCEVAddRecExpr *OtherAddRec = 1760 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx])) 1761 if (OtherAddRec->getLoop() == AddRecLoop) { 1762 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); 1763 i != e; ++i) { 1764 if (i >= AddRecOps.size()) { 1765 AddRecOps.append(OtherAddRec->op_begin()+i, 1766 OtherAddRec->op_end()); 1767 break; 1768 } 1769 AddRecOps[i] = getAddExpr(AddRecOps[i], 1770 OtherAddRec->getOperand(i)); 1771 } 1772 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx; 1773 } 1774 // Step size has changed, so we cannot guarantee no self-wraparound. 1775 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap); 1776 return getAddExpr(Ops); 1777 } 1778 1779 // Otherwise couldn't fold anything into this recurrence. Move onto the 1780 // next one. 1781 } 1782 1783 // Okay, it looks like we really DO need an add expr. Check to see if we 1784 // already have one, otherwise create a new one. 1785 FoldingSetNodeID ID; 1786 ID.AddInteger(scAddExpr); 1787 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1788 ID.AddPointer(Ops[i]); 1789 void *IP = 0; 1790 SCEVAddExpr *S = 1791 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1792 if (!S) { 1793 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 1794 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 1795 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator), 1796 O, Ops.size()); 1797 UniqueSCEVs.InsertNode(S, IP); 1798 } 1799 S->setNoWrapFlags(Flags); 1800 return S; 1801} 1802 1803/// getMulExpr - Get a canonical multiply expression, or something simpler if 1804/// possible. 1805const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops, 1806 SCEV::NoWrapFlags Flags) { 1807 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) && 1808 "only nuw or nsw allowed"); 1809 assert(!Ops.empty() && "Cannot get empty mul!"); 1810 if (Ops.size() == 1) return Ops[0]; 1811#ifndef NDEBUG 1812 Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 1813 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1814 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 1815 "SCEVMulExpr operand types don't match!"); 1816#endif 1817 1818 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW. 1819 // And vice-versa. 1820 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW; 1821 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask); 1822 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) { 1823 bool All = true; 1824 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(), 1825 E = Ops.end(); I != E; ++I) 1826 if (!isKnownNonNegative(*I)) { 1827 All = false; 1828 break; 1829 } 1830 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask); 1831 } 1832 1833 // Sort by complexity, this groups all similar expression types together. 1834 GroupByComplexity(Ops, LI); 1835 1836 // If there are any constants, fold them together. 1837 unsigned Idx = 0; 1838 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1839 1840 // C1*(C2+V) -> C1*C2 + C1*V 1841 if (Ops.size() == 2) 1842 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 1843 if (Add->getNumOperands() == 2 && 1844 isa<SCEVConstant>(Add->getOperand(0))) 1845 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 1846 getMulExpr(LHSC, Add->getOperand(1))); 1847 1848 ++Idx; 1849 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1850 // We found two constants, fold them together! 1851 ConstantInt *Fold = ConstantInt::get(getContext(), 1852 LHSC->getValue()->getValue() * 1853 RHSC->getValue()->getValue()); 1854 Ops[0] = getConstant(Fold); 1855 Ops.erase(Ops.begin()+1); // Erase the folded element 1856 if (Ops.size() == 1) return Ops[0]; 1857 LHSC = cast<SCEVConstant>(Ops[0]); 1858 } 1859 1860 // If we are left with a constant one being multiplied, strip it off. 1861 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 1862 Ops.erase(Ops.begin()); 1863 --Idx; 1864 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1865 // If we have a multiply of zero, it will always be zero. 1866 return Ops[0]; 1867 } else if (Ops[0]->isAllOnesValue()) { 1868 // If we have a mul by -1 of an add, try distributing the -1 among the 1869 // add operands. 1870 if (Ops.size() == 2) { 1871 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) { 1872 SmallVector<const SCEV *, 4> NewOps; 1873 bool AnyFolded = false; 1874 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(), 1875 E = Add->op_end(); I != E; ++I) { 1876 const SCEV *Mul = getMulExpr(Ops[0], *I); 1877 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true; 1878 NewOps.push_back(Mul); 1879 } 1880 if (AnyFolded) 1881 return getAddExpr(NewOps); 1882 } 1883 else if (const SCEVAddRecExpr * 1884 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) { 1885 // Negation preserves a recurrence's no self-wrap property. 1886 SmallVector<const SCEV *, 4> Operands; 1887 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(), 1888 E = AddRec->op_end(); I != E; ++I) { 1889 Operands.push_back(getMulExpr(Ops[0], *I)); 1890 } 1891 return getAddRecExpr(Operands, AddRec->getLoop(), 1892 AddRec->getNoWrapFlags(SCEV::FlagNW)); 1893 } 1894 } 1895 } 1896 1897 if (Ops.size() == 1) 1898 return Ops[0]; 1899 } 1900 1901 // Skip over the add expression until we get to a multiply. 1902 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1903 ++Idx; 1904 1905 // If there are mul operands inline them all into this expression. 1906 if (Idx < Ops.size()) { 1907 bool DeletedMul = false; 1908 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 1909 // If we have an mul, expand the mul operands onto the end of the operands 1910 // list. 1911 Ops.erase(Ops.begin()+Idx); 1912 Ops.append(Mul->op_begin(), Mul->op_end()); 1913 DeletedMul = true; 1914 } 1915 1916 // If we deleted at least one mul, we added operands to the end of the list, 1917 // and they are not necessarily sorted. Recurse to resort and resimplify 1918 // any operands we just acquired. 1919 if (DeletedMul) 1920 return getMulExpr(Ops); 1921 } 1922 1923 // If there are any add recurrences in the operands list, see if any other 1924 // added values are loop invariant. If so, we can fold them into the 1925 // recurrence. 1926 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1927 ++Idx; 1928 1929 // Scan over all recurrences, trying to fold loop invariants into them. 1930 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1931 // Scan all of the other operands to this mul and add them to the vector if 1932 // they are loop invariant w.r.t. the recurrence. 1933 SmallVector<const SCEV *, 8> LIOps; 1934 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1935 const Loop *AddRecLoop = AddRec->getLoop(); 1936 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1937 if (isLoopInvariant(Ops[i], AddRecLoop)) { 1938 LIOps.push_back(Ops[i]); 1939 Ops.erase(Ops.begin()+i); 1940 --i; --e; 1941 } 1942 1943 // If we found some loop invariants, fold them into the recurrence. 1944 if (!LIOps.empty()) { 1945 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 1946 SmallVector<const SCEV *, 4> NewOps; 1947 NewOps.reserve(AddRec->getNumOperands()); 1948 const SCEV *Scale = getMulExpr(LIOps); 1949 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1950 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1951 1952 // Build the new addrec. Propagate the NUW and NSW flags if both the 1953 // outer mul and the inner addrec are guaranteed to have no overflow. 1954 // 1955 // No self-wrap cannot be guaranteed after changing the step size, but 1956 // will be inferred if either NUW or NSW is true. 1957 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW)); 1958 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags); 1959 1960 // If all of the other operands were loop invariant, we are done. 1961 if (Ops.size() == 1) return NewRec; 1962 1963 // Otherwise, multiply the folded AddRec by the non-liv parts. 1964 for (unsigned i = 0;; ++i) 1965 if (Ops[i] == AddRec) { 1966 Ops[i] = NewRec; 1967 break; 1968 } 1969 return getMulExpr(Ops); 1970 } 1971 1972 // Okay, if there weren't any loop invariants to be folded, check to see if 1973 // there are multiple AddRec's with the same loop induction variable being 1974 // multiplied together. If so, we can fold them. 1975 for (unsigned OtherIdx = Idx+1; 1976 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1977 ++OtherIdx) 1978 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) { 1979 // F * G, where F = {A,+,B}<L> and G = {C,+,D}<L> --> 1980 // {A*C,+,F*D + G*B + B*D}<L> 1981 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1982 ++OtherIdx) 1983 if (const SCEVAddRecExpr *OtherAddRec = 1984 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx])) 1985 if (OtherAddRec->getLoop() == AddRecLoop) { 1986 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1987 const SCEV *NewStart = getMulExpr(F->getStart(), G->getStart()); 1988 const SCEV *B = F->getStepRecurrence(*this); 1989 const SCEV *D = G->getStepRecurrence(*this); 1990 const SCEV *NewStep = getAddExpr(getMulExpr(F, D), 1991 getMulExpr(G, B), 1992 getMulExpr(B, D)); 1993 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep, 1994 F->getLoop(), 1995 SCEV::FlagAnyWrap); 1996 if (Ops.size() == 2) return NewAddRec; 1997 Ops[Idx] = AddRec = cast<SCEVAddRecExpr>(NewAddRec); 1998 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx; 1999 } 2000 return getMulExpr(Ops); 2001 } 2002 2003 // Otherwise couldn't fold anything into this recurrence. Move onto the 2004 // next one. 2005 } 2006 2007 // Okay, it looks like we really DO need an mul expr. Check to see if we 2008 // already have one, otherwise create a new one. 2009 FoldingSetNodeID ID; 2010 ID.AddInteger(scMulExpr); 2011 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2012 ID.AddPointer(Ops[i]); 2013 void *IP = 0; 2014 SCEVMulExpr *S = 2015 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 2016 if (!S) { 2017 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2018 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2019 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator), 2020 O, Ops.size()); 2021 UniqueSCEVs.InsertNode(S, IP); 2022 } 2023 S->setNoWrapFlags(Flags); 2024 return S; 2025} 2026 2027/// getUDivExpr - Get a canonical unsigned division expression, or something 2028/// simpler if possible. 2029const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS, 2030 const SCEV *RHS) { 2031 assert(getEffectiveSCEVType(LHS->getType()) == 2032 getEffectiveSCEVType(RHS->getType()) && 2033 "SCEVUDivExpr operand types don't match!"); 2034 2035 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 2036 if (RHSC->getValue()->equalsInt(1)) 2037 return LHS; // X udiv 1 --> x 2038 // If the denominator is zero, the result of the udiv is undefined. Don't 2039 // try to analyze it, because the resolution chosen here may differ from 2040 // the resolution chosen in other parts of the compiler. 2041 if (!RHSC->getValue()->isZero()) { 2042 // Determine if the division can be folded into the operands of 2043 // its operands. 2044 // TODO: Generalize this to non-constants by using known-bits information. 2045 Type *Ty = LHS->getType(); 2046 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros(); 2047 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1; 2048 // For non-power-of-two values, effectively round the value up to the 2049 // nearest power of two. 2050 if (!RHSC->getValue()->getValue().isPowerOf2()) 2051 ++MaxShiftAmt; 2052 IntegerType *ExtTy = 2053 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt); 2054 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 2055 if (const SCEVConstant *Step = 2056 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) { 2057 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded. 2058 const APInt &StepInt = Step->getValue()->getValue(); 2059 const APInt &DivInt = RHSC->getValue()->getValue(); 2060 if (!StepInt.urem(DivInt) && 2061 getZeroExtendExpr(AR, ExtTy) == 2062 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 2063 getZeroExtendExpr(Step, ExtTy), 2064 AR->getLoop(), SCEV::FlagAnyWrap)) { 2065 SmallVector<const SCEV *, 4> Operands; 2066 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i) 2067 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS)); 2068 return getAddRecExpr(Operands, AR->getLoop(), 2069 SCEV::FlagNW); 2070 } 2071 /// Get a canonical UDivExpr for a recurrence. 2072 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0. 2073 // We can currently only fold X%N if X is constant. 2074 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart()); 2075 if (StartC && !DivInt.urem(StepInt) && 2076 getZeroExtendExpr(AR, ExtTy) == 2077 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 2078 getZeroExtendExpr(Step, ExtTy), 2079 AR->getLoop(), SCEV::FlagAnyWrap)) { 2080 const APInt &StartInt = StartC->getValue()->getValue(); 2081 const APInt &StartRem = StartInt.urem(StepInt); 2082 if (StartRem != 0) 2083 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step, 2084 AR->getLoop(), SCEV::FlagNW); 2085 } 2086 } 2087 // (A*B)/C --> A*(B/C) if safe and B/C can be folded. 2088 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) { 2089 SmallVector<const SCEV *, 4> Operands; 2090 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) 2091 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy)); 2092 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands)) 2093 // Find an operand that's safely divisible. 2094 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) { 2095 const SCEV *Op = M->getOperand(i); 2096 const SCEV *Div = getUDivExpr(Op, RHSC); 2097 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) { 2098 Operands = SmallVector<const SCEV *, 4>(M->op_begin(), 2099 M->op_end()); 2100 Operands[i] = Div; 2101 return getMulExpr(Operands); 2102 } 2103 } 2104 } 2105 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded. 2106 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) { 2107 SmallVector<const SCEV *, 4> Operands; 2108 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) 2109 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy)); 2110 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) { 2111 Operands.clear(); 2112 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { 2113 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS); 2114 if (isa<SCEVUDivExpr>(Op) || 2115 getMulExpr(Op, RHS) != A->getOperand(i)) 2116 break; 2117 Operands.push_back(Op); 2118 } 2119 if (Operands.size() == A->getNumOperands()) 2120 return getAddExpr(Operands); 2121 } 2122 } 2123 2124 // Fold if both operands are constant. 2125 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 2126 Constant *LHSCV = LHSC->getValue(); 2127 Constant *RHSCV = RHSC->getValue(); 2128 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV, 2129 RHSCV))); 2130 } 2131 } 2132 } 2133 2134 FoldingSetNodeID ID; 2135 ID.AddInteger(scUDivExpr); 2136 ID.AddPointer(LHS); 2137 ID.AddPointer(RHS); 2138 void *IP = 0; 2139 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2140 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator), 2141 LHS, RHS); 2142 UniqueSCEVs.InsertNode(S, IP); 2143 return S; 2144} 2145 2146 2147/// getAddRecExpr - Get an add recurrence expression for the specified loop. 2148/// Simplify the expression as much as possible. 2149const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step, 2150 const Loop *L, 2151 SCEV::NoWrapFlags Flags) { 2152 SmallVector<const SCEV *, 4> Operands; 2153 Operands.push_back(Start); 2154 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 2155 if (StepChrec->getLoop() == L) { 2156 Operands.append(StepChrec->op_begin(), StepChrec->op_end()); 2157 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW)); 2158 } 2159 2160 Operands.push_back(Step); 2161 return getAddRecExpr(Operands, L, Flags); 2162} 2163 2164/// getAddRecExpr - Get an add recurrence expression for the specified loop. 2165/// Simplify the expression as much as possible. 2166const SCEV * 2167ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands, 2168 const Loop *L, SCEV::NoWrapFlags Flags) { 2169 if (Operands.size() == 1) return Operands[0]; 2170#ifndef NDEBUG 2171 Type *ETy = getEffectiveSCEVType(Operands[0]->getType()); 2172 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 2173 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy && 2174 "SCEVAddRecExpr operand types don't match!"); 2175 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2176 assert(isLoopInvariant(Operands[i], L) && 2177 "SCEVAddRecExpr operand is not loop-invariant!"); 2178#endif 2179 2180 if (Operands.back()->isZero()) { 2181 Operands.pop_back(); 2182 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X 2183 } 2184 2185 // It's tempting to want to call getMaxBackedgeTakenCount count here and 2186 // use that information to infer NUW and NSW flags. However, computing a 2187 // BE count requires calling getAddRecExpr, so we may not yet have a 2188 // meaningful BE count at this point (and if we don't, we'd be stuck 2189 // with a SCEVCouldNotCompute as the cached BE count). 2190 2191 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW. 2192 // And vice-versa. 2193 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW; 2194 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask); 2195 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) { 2196 bool All = true; 2197 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(), 2198 E = Operands.end(); I != E; ++I) 2199 if (!isKnownNonNegative(*I)) { 2200 All = false; 2201 break; 2202 } 2203 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask); 2204 } 2205 2206 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 2207 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 2208 const Loop *NestedLoop = NestedAR->getLoop(); 2209 if (L->contains(NestedLoop) ? 2210 (L->getLoopDepth() < NestedLoop->getLoopDepth()) : 2211 (!NestedLoop->contains(L) && 2212 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) { 2213 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(), 2214 NestedAR->op_end()); 2215 Operands[0] = NestedAR->getStart(); 2216 // AddRecs require their operands be loop-invariant with respect to their 2217 // loops. Don't perform this transformation if it would break this 2218 // requirement. 2219 bool AllInvariant = true; 2220 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2221 if (!isLoopInvariant(Operands[i], L)) { 2222 AllInvariant = false; 2223 break; 2224 } 2225 if (AllInvariant) { 2226 // Create a recurrence for the outer loop with the same step size. 2227 // 2228 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the 2229 // inner recurrence has the same property. 2230 SCEV::NoWrapFlags OuterFlags = 2231 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags()); 2232 2233 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags); 2234 AllInvariant = true; 2235 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i) 2236 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) { 2237 AllInvariant = false; 2238 break; 2239 } 2240 if (AllInvariant) { 2241 // Ok, both add recurrences are valid after the transformation. 2242 // 2243 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if 2244 // the outer recurrence has the same property. 2245 SCEV::NoWrapFlags InnerFlags = 2246 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags); 2247 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags); 2248 } 2249 } 2250 // Reset Operands to its original state. 2251 Operands[0] = NestedAR; 2252 } 2253 } 2254 2255 // Okay, it looks like we really DO need an addrec expr. Check to see if we 2256 // already have one, otherwise create a new one. 2257 FoldingSetNodeID ID; 2258 ID.AddInteger(scAddRecExpr); 2259 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2260 ID.AddPointer(Operands[i]); 2261 ID.AddPointer(L); 2262 void *IP = 0; 2263 SCEVAddRecExpr *S = 2264 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 2265 if (!S) { 2266 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size()); 2267 std::uninitialized_copy(Operands.begin(), Operands.end(), O); 2268 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator), 2269 O, Operands.size(), L); 2270 UniqueSCEVs.InsertNode(S, IP); 2271 } 2272 S->setNoWrapFlags(Flags); 2273 return S; 2274} 2275 2276const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, 2277 const SCEV *RHS) { 2278 SmallVector<const SCEV *, 2> Ops; 2279 Ops.push_back(LHS); 2280 Ops.push_back(RHS); 2281 return getSMaxExpr(Ops); 2282} 2283 2284const SCEV * 2285ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2286 assert(!Ops.empty() && "Cannot get empty smax!"); 2287 if (Ops.size() == 1) return Ops[0]; 2288#ifndef NDEBUG 2289 Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 2290 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2291 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 2292 "SCEVSMaxExpr operand types don't match!"); 2293#endif 2294 2295 // Sort by complexity, this groups all similar expression types together. 2296 GroupByComplexity(Ops, LI); 2297 2298 // If there are any constants, fold them together. 2299 unsigned Idx = 0; 2300 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2301 ++Idx; 2302 assert(Idx < Ops.size()); 2303 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2304 // We found two constants, fold them together! 2305 ConstantInt *Fold = ConstantInt::get(getContext(), 2306 APIntOps::smax(LHSC->getValue()->getValue(), 2307 RHSC->getValue()->getValue())); 2308 Ops[0] = getConstant(Fold); 2309 Ops.erase(Ops.begin()+1); // Erase the folded element 2310 if (Ops.size() == 1) return Ops[0]; 2311 LHSC = cast<SCEVConstant>(Ops[0]); 2312 } 2313 2314 // If we are left with a constant minimum-int, strip it off. 2315 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 2316 Ops.erase(Ops.begin()); 2317 --Idx; 2318 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) { 2319 // If we have an smax with a constant maximum-int, it will always be 2320 // maximum-int. 2321 return Ops[0]; 2322 } 2323 2324 if (Ops.size() == 1) return Ops[0]; 2325 } 2326 2327 // Find the first SMax 2328 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 2329 ++Idx; 2330 2331 // Check to see if one of the operands is an SMax. If so, expand its operands 2332 // onto our operand list, and recurse to simplify. 2333 if (Idx < Ops.size()) { 2334 bool DeletedSMax = false; 2335 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 2336 Ops.erase(Ops.begin()+Idx); 2337 Ops.append(SMax->op_begin(), SMax->op_end()); 2338 DeletedSMax = true; 2339 } 2340 2341 if (DeletedSMax) 2342 return getSMaxExpr(Ops); 2343 } 2344 2345 // Okay, check to see if the same value occurs in the operand list twice. If 2346 // so, delete one. Since we sorted the list, these values are required to 2347 // be adjacent. 2348 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2349 // X smax Y smax Y --> X smax Y 2350 // X smax Y --> X, if X is always greater than Y 2351 if (Ops[i] == Ops[i+1] || 2352 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) { 2353 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 2354 --i; --e; 2355 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) { 2356 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2357 --i; --e; 2358 } 2359 2360 if (Ops.size() == 1) return Ops[0]; 2361 2362 assert(!Ops.empty() && "Reduced smax down to nothing!"); 2363 2364 // Okay, it looks like we really DO need an smax expr. Check to see if we 2365 // already have one, otherwise create a new one. 2366 FoldingSetNodeID ID; 2367 ID.AddInteger(scSMaxExpr); 2368 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2369 ID.AddPointer(Ops[i]); 2370 void *IP = 0; 2371 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2372 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2373 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2374 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator), 2375 O, Ops.size()); 2376 UniqueSCEVs.InsertNode(S, IP); 2377 return S; 2378} 2379 2380const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, 2381 const SCEV *RHS) { 2382 SmallVector<const SCEV *, 2> Ops; 2383 Ops.push_back(LHS); 2384 Ops.push_back(RHS); 2385 return getUMaxExpr(Ops); 2386} 2387 2388const SCEV * 2389ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2390 assert(!Ops.empty() && "Cannot get empty umax!"); 2391 if (Ops.size() == 1) return Ops[0]; 2392#ifndef NDEBUG 2393 Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 2394 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2395 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 2396 "SCEVUMaxExpr operand types don't match!"); 2397#endif 2398 2399 // Sort by complexity, this groups all similar expression types together. 2400 GroupByComplexity(Ops, LI); 2401 2402 // If there are any constants, fold them together. 2403 unsigned Idx = 0; 2404 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2405 ++Idx; 2406 assert(Idx < Ops.size()); 2407 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2408 // We found two constants, fold them together! 2409 ConstantInt *Fold = ConstantInt::get(getContext(), 2410 APIntOps::umax(LHSC->getValue()->getValue(), 2411 RHSC->getValue()->getValue())); 2412 Ops[0] = getConstant(Fold); 2413 Ops.erase(Ops.begin()+1); // Erase the folded element 2414 if (Ops.size() == 1) return Ops[0]; 2415 LHSC = cast<SCEVConstant>(Ops[0]); 2416 } 2417 2418 // If we are left with a constant minimum-int, strip it off. 2419 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 2420 Ops.erase(Ops.begin()); 2421 --Idx; 2422 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) { 2423 // If we have an umax with a constant maximum-int, it will always be 2424 // maximum-int. 2425 return Ops[0]; 2426 } 2427 2428 if (Ops.size() == 1) return Ops[0]; 2429 } 2430 2431 // Find the first UMax 2432 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 2433 ++Idx; 2434 2435 // Check to see if one of the operands is a UMax. If so, expand its operands 2436 // onto our operand list, and recurse to simplify. 2437 if (Idx < Ops.size()) { 2438 bool DeletedUMax = false; 2439 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 2440 Ops.erase(Ops.begin()+Idx); 2441 Ops.append(UMax->op_begin(), UMax->op_end()); 2442 DeletedUMax = true; 2443 } 2444 2445 if (DeletedUMax) 2446 return getUMaxExpr(Ops); 2447 } 2448 2449 // Okay, check to see if the same value occurs in the operand list twice. If 2450 // so, delete one. Since we sorted the list, these values are required to 2451 // be adjacent. 2452 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2453 // X umax Y umax Y --> X umax Y 2454 // X umax Y --> X, if X is always greater than Y 2455 if (Ops[i] == Ops[i+1] || 2456 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) { 2457 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 2458 --i; --e; 2459 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) { 2460 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2461 --i; --e; 2462 } 2463 2464 if (Ops.size() == 1) return Ops[0]; 2465 2466 assert(!Ops.empty() && "Reduced umax down to nothing!"); 2467 2468 // Okay, it looks like we really DO need a umax expr. Check to see if we 2469 // already have one, otherwise create a new one. 2470 FoldingSetNodeID ID; 2471 ID.AddInteger(scUMaxExpr); 2472 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2473 ID.AddPointer(Ops[i]); 2474 void *IP = 0; 2475 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2476 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2477 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2478 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator), 2479 O, Ops.size()); 2480 UniqueSCEVs.InsertNode(S, IP); 2481 return S; 2482} 2483 2484const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS, 2485 const SCEV *RHS) { 2486 // ~smax(~x, ~y) == smin(x, y). 2487 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2488} 2489 2490const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS, 2491 const SCEV *RHS) { 2492 // ~umax(~x, ~y) == umin(x, y) 2493 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2494} 2495 2496const SCEV *ScalarEvolution::getSizeOfExpr(Type *AllocTy) { 2497 // If we have TargetData, we can bypass creating a target-independent 2498 // constant expression and then folding it back into a ConstantInt. 2499 // This is just a compile-time optimization. 2500 if (TD) 2501 return getConstant(TD->getIntPtrType(getContext()), 2502 TD->getTypeAllocSize(AllocTy)); 2503 2504 Constant *C = ConstantExpr::getSizeOf(AllocTy); 2505 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2506 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2507 C = Folded; 2508 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2509 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2510} 2511 2512const SCEV *ScalarEvolution::getAlignOfExpr(Type *AllocTy) { 2513 Constant *C = ConstantExpr::getAlignOf(AllocTy); 2514 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2515 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2516 C = Folded; 2517 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2518 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2519} 2520 2521const SCEV *ScalarEvolution::getOffsetOfExpr(StructType *STy, 2522 unsigned FieldNo) { 2523 // If we have TargetData, we can bypass creating a target-independent 2524 // constant expression and then folding it back into a ConstantInt. 2525 // This is just a compile-time optimization. 2526 if (TD) 2527 return getConstant(TD->getIntPtrType(getContext()), 2528 TD->getStructLayout(STy)->getElementOffset(FieldNo)); 2529 2530 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo); 2531 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2532 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2533 C = Folded; 2534 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy)); 2535 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2536} 2537 2538const SCEV *ScalarEvolution::getOffsetOfExpr(Type *CTy, 2539 Constant *FieldNo) { 2540 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo); 2541 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2542 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2543 C = Folded; 2544 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy)); 2545 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2546} 2547 2548const SCEV *ScalarEvolution::getUnknown(Value *V) { 2549 // Don't attempt to do anything other than create a SCEVUnknown object 2550 // here. createSCEV only calls getUnknown after checking for all other 2551 // interesting possibilities, and any other code that calls getUnknown 2552 // is doing so in order to hide a value from SCEV canonicalization. 2553 2554 FoldingSetNodeID ID; 2555 ID.AddInteger(scUnknown); 2556 ID.AddPointer(V); 2557 void *IP = 0; 2558 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) { 2559 assert(cast<SCEVUnknown>(S)->getValue() == V && 2560 "Stale SCEVUnknown in uniquing map!"); 2561 return S; 2562 } 2563 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this, 2564 FirstUnknown); 2565 FirstUnknown = cast<SCEVUnknown>(S); 2566 UniqueSCEVs.InsertNode(S, IP); 2567 return S; 2568} 2569 2570//===----------------------------------------------------------------------===// 2571// Basic SCEV Analysis and PHI Idiom Recognition Code 2572// 2573 2574/// isSCEVable - Test if values of the given type are analyzable within 2575/// the SCEV framework. This primarily includes integer types, and it 2576/// can optionally include pointer types if the ScalarEvolution class 2577/// has access to target-specific information. 2578bool ScalarEvolution::isSCEVable(Type *Ty) const { 2579 // Integers and pointers are always SCEVable. 2580 return Ty->isIntegerTy() || Ty->isPointerTy(); 2581} 2582 2583/// getTypeSizeInBits - Return the size in bits of the specified type, 2584/// for which isSCEVable must return true. 2585uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const { 2586 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2587 2588 // If we have a TargetData, use it! 2589 if (TD) 2590 return TD->getTypeSizeInBits(Ty); 2591 2592 // Integer types have fixed sizes. 2593 if (Ty->isIntegerTy()) 2594 return Ty->getPrimitiveSizeInBits(); 2595 2596 // The only other support type is pointer. Without TargetData, conservatively 2597 // assume pointers are 64-bit. 2598 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!"); 2599 return 64; 2600} 2601 2602/// getEffectiveSCEVType - Return a type with the same bitwidth as 2603/// the given type and which represents how SCEV will treat the given 2604/// type, for which isSCEVable must return true. For pointer types, 2605/// this is the pointer-sized integer type. 2606Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const { 2607 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2608 2609 if (Ty->isIntegerTy()) 2610 return Ty; 2611 2612 // The only other support type is pointer. 2613 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!"); 2614 if (TD) return TD->getIntPtrType(getContext()); 2615 2616 // Without TargetData, conservatively assume pointers are 64-bit. 2617 return Type::getInt64Ty(getContext()); 2618} 2619 2620const SCEV *ScalarEvolution::getCouldNotCompute() { 2621 return &CouldNotCompute; 2622} 2623 2624/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 2625/// expression and create a new one. 2626const SCEV *ScalarEvolution::getSCEV(Value *V) { 2627 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 2628 2629 ValueExprMapType::const_iterator I = ValueExprMap.find(V); 2630 if (I != ValueExprMap.end()) return I->second; 2631 const SCEV *S = createSCEV(V); 2632 2633 // The process of creating a SCEV for V may have caused other SCEVs 2634 // to have been created, so it's necessary to insert the new entry 2635 // from scratch, rather than trying to remember the insert position 2636 // above. 2637 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S)); 2638 return S; 2639} 2640 2641/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 2642/// 2643const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) { 2644 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2645 return getConstant( 2646 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue()))); 2647 2648 Type *Ty = V->getType(); 2649 Ty = getEffectiveSCEVType(Ty); 2650 return getMulExpr(V, 2651 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)))); 2652} 2653 2654/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 2655const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) { 2656 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2657 return getConstant( 2658 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue()))); 2659 2660 Type *Ty = V->getType(); 2661 Ty = getEffectiveSCEVType(Ty); 2662 const SCEV *AllOnes = 2663 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))); 2664 return getMinusSCEV(AllOnes, V); 2665} 2666 2667/// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1. 2668const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS, 2669 SCEV::NoWrapFlags Flags) { 2670 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW"); 2671 2672 // Fast path: X - X --> 0. 2673 if (LHS == RHS) 2674 return getConstant(LHS->getType(), 0); 2675 2676 // X - Y --> X + -Y 2677 return getAddExpr(LHS, getNegativeSCEV(RHS), Flags); 2678} 2679 2680/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 2681/// input value to the specified type. If the type must be extended, it is zero 2682/// extended. 2683const SCEV * 2684ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) { 2685 Type *SrcTy = V->getType(); 2686 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2687 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2688 "Cannot truncate or zero extend with non-integer arguments!"); 2689 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2690 return V; // No conversion 2691 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2692 return getTruncateExpr(V, Ty); 2693 return getZeroExtendExpr(V, Ty); 2694} 2695 2696/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 2697/// input value to the specified type. If the type must be extended, it is sign 2698/// extended. 2699const SCEV * 2700ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, 2701 Type *Ty) { 2702 Type *SrcTy = V->getType(); 2703 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2704 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2705 "Cannot truncate or zero extend with non-integer arguments!"); 2706 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2707 return V; // No conversion 2708 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2709 return getTruncateExpr(V, Ty); 2710 return getSignExtendExpr(V, Ty); 2711} 2712 2713/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the 2714/// input value to the specified type. If the type must be extended, it is zero 2715/// extended. The conversion must not be narrowing. 2716const SCEV * 2717ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) { 2718 Type *SrcTy = V->getType(); 2719 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2720 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2721 "Cannot noop or zero extend with non-integer arguments!"); 2722 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2723 "getNoopOrZeroExtend cannot truncate!"); 2724 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2725 return V; // No conversion 2726 return getZeroExtendExpr(V, Ty); 2727} 2728 2729/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the 2730/// input value to the specified type. If the type must be extended, it is sign 2731/// extended. The conversion must not be narrowing. 2732const SCEV * 2733ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) { 2734 Type *SrcTy = V->getType(); 2735 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2736 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2737 "Cannot noop or sign extend with non-integer arguments!"); 2738 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2739 "getNoopOrSignExtend cannot truncate!"); 2740 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2741 return V; // No conversion 2742 return getSignExtendExpr(V, Ty); 2743} 2744 2745/// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of 2746/// the input value to the specified type. If the type must be extended, 2747/// it is extended with unspecified bits. The conversion must not be 2748/// narrowing. 2749const SCEV * 2750ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) { 2751 Type *SrcTy = V->getType(); 2752 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2753 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2754 "Cannot noop or any extend with non-integer arguments!"); 2755 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2756 "getNoopOrAnyExtend cannot truncate!"); 2757 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2758 return V; // No conversion 2759 return getAnyExtendExpr(V, Ty); 2760} 2761 2762/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the 2763/// input value to the specified type. The conversion must not be widening. 2764const SCEV * 2765ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) { 2766 Type *SrcTy = V->getType(); 2767 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2768 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2769 "Cannot truncate or noop with non-integer arguments!"); 2770 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && 2771 "getTruncateOrNoop cannot extend!"); 2772 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2773 return V; // No conversion 2774 return getTruncateExpr(V, Ty); 2775} 2776 2777/// getUMaxFromMismatchedTypes - Promote the operands to the wider of 2778/// the types using zero-extension, and then perform a umax operation 2779/// with them. 2780const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS, 2781 const SCEV *RHS) { 2782 const SCEV *PromotedLHS = LHS; 2783 const SCEV *PromotedRHS = RHS; 2784 2785 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2786 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2787 else 2788 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2789 2790 return getUMaxExpr(PromotedLHS, PromotedRHS); 2791} 2792 2793/// getUMinFromMismatchedTypes - Promote the operands to the wider of 2794/// the types using zero-extension, and then perform a umin operation 2795/// with them. 2796const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS, 2797 const SCEV *RHS) { 2798 const SCEV *PromotedLHS = LHS; 2799 const SCEV *PromotedRHS = RHS; 2800 2801 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2802 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2803 else 2804 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2805 2806 return getUMinExpr(PromotedLHS, PromotedRHS); 2807} 2808 2809/// getPointerBase - Transitively follow the chain of pointer-type operands 2810/// until reaching a SCEV that does not have a single pointer operand. This 2811/// returns a SCEVUnknown pointer for well-formed pointer-type expressions, 2812/// but corner cases do exist. 2813const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) { 2814 // A pointer operand may evaluate to a nonpointer expression, such as null. 2815 if (!V->getType()->isPointerTy()) 2816 return V; 2817 2818 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) { 2819 return getPointerBase(Cast->getOperand()); 2820 } 2821 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) { 2822 const SCEV *PtrOp = 0; 2823 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 2824 I != E; ++I) { 2825 if ((*I)->getType()->isPointerTy()) { 2826 // Cannot find the base of an expression with multiple pointer operands. 2827 if (PtrOp) 2828 return V; 2829 PtrOp = *I; 2830 } 2831 } 2832 if (!PtrOp) 2833 return V; 2834 return getPointerBase(PtrOp); 2835 } 2836 return V; 2837} 2838 2839/// PushDefUseChildren - Push users of the given Instruction 2840/// onto the given Worklist. 2841static void 2842PushDefUseChildren(Instruction *I, 2843 SmallVectorImpl<Instruction *> &Worklist) { 2844 // Push the def-use children onto the Worklist stack. 2845 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end(); 2846 UI != UE; ++UI) 2847 Worklist.push_back(cast<Instruction>(*UI)); 2848} 2849 2850/// ForgetSymbolicValue - This looks up computed SCEV values for all 2851/// instructions that depend on the given instruction and removes them from 2852/// the ValueExprMapType map if they reference SymName. This is used during PHI 2853/// resolution. 2854void 2855ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) { 2856 SmallVector<Instruction *, 16> Worklist; 2857 PushDefUseChildren(PN, Worklist); 2858 2859 SmallPtrSet<Instruction *, 8> Visited; 2860 Visited.insert(PN); 2861 while (!Worklist.empty()) { 2862 Instruction *I = Worklist.pop_back_val(); 2863 if (!Visited.insert(I)) continue; 2864 2865 ValueExprMapType::iterator It = 2866 ValueExprMap.find(static_cast<Value *>(I)); 2867 if (It != ValueExprMap.end()) { 2868 const SCEV *Old = It->second; 2869 2870 // Short-circuit the def-use traversal if the symbolic name 2871 // ceases to appear in expressions. 2872 if (Old != SymName && !hasOperand(Old, SymName)) 2873 continue; 2874 2875 // SCEVUnknown for a PHI either means that it has an unrecognized 2876 // structure, it's a PHI that's in the progress of being computed 2877 // by createNodeForPHI, or it's a single-value PHI. In the first case, 2878 // additional loop trip count information isn't going to change anything. 2879 // In the second case, createNodeForPHI will perform the necessary 2880 // updates on its own when it gets to that point. In the third, we do 2881 // want to forget the SCEVUnknown. 2882 if (!isa<PHINode>(I) || 2883 !isa<SCEVUnknown>(Old) || 2884 (I != PN && Old == SymName)) { 2885 forgetMemoizedResults(Old); 2886 ValueExprMap.erase(It); 2887 } 2888 } 2889 2890 PushDefUseChildren(I, Worklist); 2891 } 2892} 2893 2894/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 2895/// a loop header, making it a potential recurrence, or it doesn't. 2896/// 2897const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) { 2898 if (const Loop *L = LI->getLoopFor(PN->getParent())) 2899 if (L->getHeader() == PN->getParent()) { 2900 // The loop may have multiple entrances or multiple exits; we can analyze 2901 // this phi as an addrec if it has a unique entry value and a unique 2902 // backedge value. 2903 Value *BEValueV = 0, *StartValueV = 0; 2904 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) { 2905 Value *V = PN->getIncomingValue(i); 2906 if (L->contains(PN->getIncomingBlock(i))) { 2907 if (!BEValueV) { 2908 BEValueV = V; 2909 } else if (BEValueV != V) { 2910 BEValueV = 0; 2911 break; 2912 } 2913 } else if (!StartValueV) { 2914 StartValueV = V; 2915 } else if (StartValueV != V) { 2916 StartValueV = 0; 2917 break; 2918 } 2919 } 2920 if (BEValueV && StartValueV) { 2921 // While we are analyzing this PHI node, handle its value symbolically. 2922 const SCEV *SymbolicName = getUnknown(PN); 2923 assert(ValueExprMap.find(PN) == ValueExprMap.end() && 2924 "PHI node already processed?"); 2925 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName)); 2926 2927 // Using this symbolic name for the PHI, analyze the value coming around 2928 // the back-edge. 2929 const SCEV *BEValue = getSCEV(BEValueV); 2930 2931 // NOTE: If BEValue is loop invariant, we know that the PHI node just 2932 // has a special value for the first iteration of the loop. 2933 2934 // If the value coming around the backedge is an add with the symbolic 2935 // value we just inserted, then we found a simple induction variable! 2936 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 2937 // If there is a single occurrence of the symbolic value, replace it 2938 // with a recurrence. 2939 unsigned FoundIndex = Add->getNumOperands(); 2940 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2941 if (Add->getOperand(i) == SymbolicName) 2942 if (FoundIndex == e) { 2943 FoundIndex = i; 2944 break; 2945 } 2946 2947 if (FoundIndex != Add->getNumOperands()) { 2948 // Create an add with everything but the specified operand. 2949 SmallVector<const SCEV *, 8> Ops; 2950 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2951 if (i != FoundIndex) 2952 Ops.push_back(Add->getOperand(i)); 2953 const SCEV *Accum = getAddExpr(Ops); 2954 2955 // This is not a valid addrec if the step amount is varying each 2956 // loop iteration, but is not itself an addrec in this loop. 2957 if (isLoopInvariant(Accum, L) || 2958 (isa<SCEVAddRecExpr>(Accum) && 2959 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 2960 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap; 2961 2962 // If the increment doesn't overflow, then neither the addrec nor 2963 // the post-increment will overflow. 2964 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) { 2965 if (OBO->hasNoUnsignedWrap()) 2966 Flags = setFlags(Flags, SCEV::FlagNUW); 2967 if (OBO->hasNoSignedWrap()) 2968 Flags = setFlags(Flags, SCEV::FlagNSW); 2969 } else if (const GEPOperator *GEP = 2970 dyn_cast<GEPOperator>(BEValueV)) { 2971 // If the increment is an inbounds GEP, then we know the address 2972 // space cannot be wrapped around. We cannot make any guarantee 2973 // about signed or unsigned overflow because pointers are 2974 // unsigned but we may have a negative index from the base 2975 // pointer. 2976 if (GEP->isInBounds()) 2977 Flags = setFlags(Flags, SCEV::FlagNW); 2978 } 2979 2980 const SCEV *StartVal = getSCEV(StartValueV); 2981 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags); 2982 2983 // Since the no-wrap flags are on the increment, they apply to the 2984 // post-incremented value as well. 2985 if (isLoopInvariant(Accum, L)) 2986 (void)getAddRecExpr(getAddExpr(StartVal, Accum), 2987 Accum, L, Flags); 2988 2989 // Okay, for the entire analysis of this edge we assumed the PHI 2990 // to be symbolic. We now need to go back and purge all of the 2991 // entries for the scalars that use the symbolic expression. 2992 ForgetSymbolicName(PN, SymbolicName); 2993 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV; 2994 return PHISCEV; 2995 } 2996 } 2997 } else if (const SCEVAddRecExpr *AddRec = 2998 dyn_cast<SCEVAddRecExpr>(BEValue)) { 2999 // Otherwise, this could be a loop like this: 3000 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 3001 // In this case, j = {1,+,1} and BEValue is j. 3002 // Because the other in-value of i (0) fits the evolution of BEValue 3003 // i really is an addrec evolution. 3004 if (AddRec->getLoop() == L && AddRec->isAffine()) { 3005 const SCEV *StartVal = getSCEV(StartValueV); 3006 3007 // If StartVal = j.start - j.stride, we can use StartVal as the 3008 // initial step of the addrec evolution. 3009 if (StartVal == getMinusSCEV(AddRec->getOperand(0), 3010 AddRec->getOperand(1))) { 3011 // FIXME: For constant StartVal, we should be able to infer 3012 // no-wrap flags. 3013 const SCEV *PHISCEV = 3014 getAddRecExpr(StartVal, AddRec->getOperand(1), L, 3015 SCEV::FlagAnyWrap); 3016 3017 // Okay, for the entire analysis of this edge we assumed the PHI 3018 // to be symbolic. We now need to go back and purge all of the 3019 // entries for the scalars that use the symbolic expression. 3020 ForgetSymbolicName(PN, SymbolicName); 3021 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV; 3022 return PHISCEV; 3023 } 3024 } 3025 } 3026 } 3027 } 3028 3029 // If the PHI has a single incoming value, follow that value, unless the 3030 // PHI's incoming blocks are in a different loop, in which case doing so 3031 // risks breaking LCSSA form. Instcombine would normally zap these, but 3032 // it doesn't have DominatorTree information, so it may miss cases. 3033 if (Value *V = SimplifyInstruction(PN, TD, DT)) 3034 if (LI->replacementPreservesLCSSAForm(PN, V)) 3035 return getSCEV(V); 3036 3037 // If it's not a loop phi, we can't handle it yet. 3038 return getUnknown(PN); 3039} 3040 3041/// createNodeForGEP - Expand GEP instructions into add and multiply 3042/// operations. This allows them to be analyzed by regular SCEV code. 3043/// 3044const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) { 3045 3046 // Don't blindly transfer the inbounds flag from the GEP instruction to the 3047 // Add expression, because the Instruction may be guarded by control flow 3048 // and the no-overflow bits may not be valid for the expression in any 3049 // context. 3050 bool isInBounds = GEP->isInBounds(); 3051 3052 Type *IntPtrTy = getEffectiveSCEVType(GEP->getType()); 3053 Value *Base = GEP->getOperand(0); 3054 // Don't attempt to analyze GEPs over unsized objects. 3055 if (!cast<PointerType>(Base->getType())->getElementType()->isSized()) 3056 return getUnknown(GEP); 3057 const SCEV *TotalOffset = getConstant(IntPtrTy, 0); 3058 gep_type_iterator GTI = gep_type_begin(GEP); 3059 for (GetElementPtrInst::op_iterator I = llvm::next(GEP->op_begin()), 3060 E = GEP->op_end(); 3061 I != E; ++I) { 3062 Value *Index = *I; 3063 // Compute the (potentially symbolic) offset in bytes for this index. 3064 if (StructType *STy = dyn_cast<StructType>(*GTI++)) { 3065 // For a struct, add the member offset. 3066 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 3067 const SCEV *FieldOffset = getOffsetOfExpr(STy, FieldNo); 3068 3069 // Add the field offset to the running total offset. 3070 TotalOffset = getAddExpr(TotalOffset, FieldOffset); 3071 } else { 3072 // For an array, add the element offset, explicitly scaled. 3073 const SCEV *ElementSize = getSizeOfExpr(*GTI); 3074 const SCEV *IndexS = getSCEV(Index); 3075 // Getelementptr indices are signed. 3076 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy); 3077 3078 // Multiply the index by the element size to compute the element offset. 3079 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize, 3080 isInBounds ? SCEV::FlagNSW : 3081 SCEV::FlagAnyWrap); 3082 3083 // Add the element offset to the running total offset. 3084 TotalOffset = getAddExpr(TotalOffset, LocalOffset); 3085 } 3086 } 3087 3088 // Get the SCEV for the GEP base. 3089 const SCEV *BaseS = getSCEV(Base); 3090 3091 // Add the total offset from all the GEP indices to the base. 3092 return getAddExpr(BaseS, TotalOffset, 3093 isInBounds ? SCEV::FlagNSW : SCEV::FlagAnyWrap); 3094} 3095 3096/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 3097/// guaranteed to end in (at every loop iteration). It is, at the same time, 3098/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 3099/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 3100uint32_t 3101ScalarEvolution::GetMinTrailingZeros(const SCEV *S) { 3102 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3103 return C->getValue()->getValue().countTrailingZeros(); 3104 3105 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 3106 return std::min(GetMinTrailingZeros(T->getOperand()), 3107 (uint32_t)getTypeSizeInBits(T->getType())); 3108 3109 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 3110 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 3111 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 3112 getTypeSizeInBits(E->getType()) : OpRes; 3113 } 3114 3115 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 3116 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 3117 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 3118 getTypeSizeInBits(E->getType()) : OpRes; 3119 } 3120 3121 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 3122 // The result is the min of all operands results. 3123 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 3124 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 3125 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 3126 return MinOpRes; 3127 } 3128 3129 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 3130 // The result is the sum of all operands results. 3131 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 3132 uint32_t BitWidth = getTypeSizeInBits(M->getType()); 3133 for (unsigned i = 1, e = M->getNumOperands(); 3134 SumOpRes != BitWidth && i != e; ++i) 3135 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 3136 BitWidth); 3137 return SumOpRes; 3138 } 3139 3140 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 3141 // The result is the min of all operands results. 3142 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 3143 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 3144 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 3145 return MinOpRes; 3146 } 3147 3148 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 3149 // The result is the min of all operands results. 3150 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 3151 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 3152 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 3153 return MinOpRes; 3154 } 3155 3156 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 3157 // The result is the min of all operands results. 3158 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 3159 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 3160 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 3161 return MinOpRes; 3162 } 3163 3164 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3165 // For a SCEVUnknown, ask ValueTracking. 3166 unsigned BitWidth = getTypeSizeInBits(U->getType()); 3167 APInt Mask = APInt::getAllOnesValue(BitWidth); 3168 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 3169 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones); 3170 return Zeros.countTrailingOnes(); 3171 } 3172 3173 // SCEVUDivExpr 3174 return 0; 3175} 3176 3177/// getUnsignedRange - Determine the unsigned range for a particular SCEV. 3178/// 3179ConstantRange 3180ScalarEvolution::getUnsignedRange(const SCEV *S) { 3181 // See if we've computed this range already. 3182 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S); 3183 if (I != UnsignedRanges.end()) 3184 return I->second; 3185 3186 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3187 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue())); 3188 3189 unsigned BitWidth = getTypeSizeInBits(S->getType()); 3190 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 3191 3192 // If the value has known zeros, the maximum unsigned value will have those 3193 // known zeros as well. 3194 uint32_t TZ = GetMinTrailingZeros(S); 3195 if (TZ != 0) 3196 ConservativeResult = 3197 ConstantRange(APInt::getMinValue(BitWidth), 3198 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1); 3199 3200 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 3201 ConstantRange X = getUnsignedRange(Add->getOperand(0)); 3202 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 3203 X = X.add(getUnsignedRange(Add->getOperand(i))); 3204 return setUnsignedRange(Add, ConservativeResult.intersectWith(X)); 3205 } 3206 3207 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 3208 ConstantRange X = getUnsignedRange(Mul->getOperand(0)); 3209 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 3210 X = X.multiply(getUnsignedRange(Mul->getOperand(i))); 3211 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X)); 3212 } 3213 3214 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 3215 ConstantRange X = getUnsignedRange(SMax->getOperand(0)); 3216 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 3217 X = X.smax(getUnsignedRange(SMax->getOperand(i))); 3218 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X)); 3219 } 3220 3221 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 3222 ConstantRange X = getUnsignedRange(UMax->getOperand(0)); 3223 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 3224 X = X.umax(getUnsignedRange(UMax->getOperand(i))); 3225 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X)); 3226 } 3227 3228 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 3229 ConstantRange X = getUnsignedRange(UDiv->getLHS()); 3230 ConstantRange Y = getUnsignedRange(UDiv->getRHS()); 3231 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y))); 3232 } 3233 3234 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 3235 ConstantRange X = getUnsignedRange(ZExt->getOperand()); 3236 return setUnsignedRange(ZExt, 3237 ConservativeResult.intersectWith(X.zeroExtend(BitWidth))); 3238 } 3239 3240 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 3241 ConstantRange X = getUnsignedRange(SExt->getOperand()); 3242 return setUnsignedRange(SExt, 3243 ConservativeResult.intersectWith(X.signExtend(BitWidth))); 3244 } 3245 3246 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 3247 ConstantRange X = getUnsignedRange(Trunc->getOperand()); 3248 return setUnsignedRange(Trunc, 3249 ConservativeResult.intersectWith(X.truncate(BitWidth))); 3250 } 3251 3252 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 3253 // If there's no unsigned wrap, the value will never be less than its 3254 // initial value. 3255 if (AddRec->getNoWrapFlags(SCEV::FlagNUW)) 3256 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart())) 3257 if (!C->getValue()->isZero()) 3258 ConservativeResult = 3259 ConservativeResult.intersectWith( 3260 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0))); 3261 3262 // TODO: non-affine addrec 3263 if (AddRec->isAffine()) { 3264 Type *Ty = AddRec->getType(); 3265 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3266 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3267 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3268 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3269 3270 const SCEV *Start = AddRec->getStart(); 3271 const SCEV *Step = AddRec->getStepRecurrence(*this); 3272 3273 ConstantRange StartRange = getUnsignedRange(Start); 3274 ConstantRange StepRange = getSignedRange(Step); 3275 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); 3276 ConstantRange EndRange = 3277 StartRange.add(MaxBECountRange.multiply(StepRange)); 3278 3279 // Check for overflow. This must be done with ConstantRange arithmetic 3280 // because we could be called from within the ScalarEvolution overflow 3281 // checking code. 3282 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1); 3283 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1); 3284 ConstantRange ExtMaxBECountRange = 3285 MaxBECountRange.zextOrTrunc(BitWidth*2+1); 3286 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1); 3287 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) != 3288 ExtEndRange) 3289 return setUnsignedRange(AddRec, ConservativeResult); 3290 3291 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(), 3292 EndRange.getUnsignedMin()); 3293 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(), 3294 EndRange.getUnsignedMax()); 3295 if (Min.isMinValue() && Max.isMaxValue()) 3296 return setUnsignedRange(AddRec, ConservativeResult); 3297 return setUnsignedRange(AddRec, 3298 ConservativeResult.intersectWith(ConstantRange(Min, Max+1))); 3299 } 3300 } 3301 3302 return setUnsignedRange(AddRec, ConservativeResult); 3303 } 3304 3305 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3306 // For a SCEVUnknown, ask ValueTracking. 3307 APInt Mask = APInt::getAllOnesValue(BitWidth); 3308 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 3309 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD); 3310 if (Ones == ~Zeros + 1) 3311 return setUnsignedRange(U, ConservativeResult); 3312 return setUnsignedRange(U, 3313 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1))); 3314 } 3315 3316 return setUnsignedRange(S, ConservativeResult); 3317} 3318 3319/// getSignedRange - Determine the signed range for a particular SCEV. 3320/// 3321ConstantRange 3322ScalarEvolution::getSignedRange(const SCEV *S) { 3323 // See if we've computed this range already. 3324 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S); 3325 if (I != SignedRanges.end()) 3326 return I->second; 3327 3328 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3329 return setSignedRange(C, ConstantRange(C->getValue()->getValue())); 3330 3331 unsigned BitWidth = getTypeSizeInBits(S->getType()); 3332 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 3333 3334 // If the value has known zeros, the maximum signed value will have those 3335 // known zeros as well. 3336 uint32_t TZ = GetMinTrailingZeros(S); 3337 if (TZ != 0) 3338 ConservativeResult = 3339 ConstantRange(APInt::getSignedMinValue(BitWidth), 3340 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1); 3341 3342 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 3343 ConstantRange X = getSignedRange(Add->getOperand(0)); 3344 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 3345 X = X.add(getSignedRange(Add->getOperand(i))); 3346 return setSignedRange(Add, ConservativeResult.intersectWith(X)); 3347 } 3348 3349 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 3350 ConstantRange X = getSignedRange(Mul->getOperand(0)); 3351 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 3352 X = X.multiply(getSignedRange(Mul->getOperand(i))); 3353 return setSignedRange(Mul, ConservativeResult.intersectWith(X)); 3354 } 3355 3356 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 3357 ConstantRange X = getSignedRange(SMax->getOperand(0)); 3358 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 3359 X = X.smax(getSignedRange(SMax->getOperand(i))); 3360 return setSignedRange(SMax, ConservativeResult.intersectWith(X)); 3361 } 3362 3363 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 3364 ConstantRange X = getSignedRange(UMax->getOperand(0)); 3365 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 3366 X = X.umax(getSignedRange(UMax->getOperand(i))); 3367 return setSignedRange(UMax, ConservativeResult.intersectWith(X)); 3368 } 3369 3370 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 3371 ConstantRange X = getSignedRange(UDiv->getLHS()); 3372 ConstantRange Y = getSignedRange(UDiv->getRHS()); 3373 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y))); 3374 } 3375 3376 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 3377 ConstantRange X = getSignedRange(ZExt->getOperand()); 3378 return setSignedRange(ZExt, 3379 ConservativeResult.intersectWith(X.zeroExtend(BitWidth))); 3380 } 3381 3382 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 3383 ConstantRange X = getSignedRange(SExt->getOperand()); 3384 return setSignedRange(SExt, 3385 ConservativeResult.intersectWith(X.signExtend(BitWidth))); 3386 } 3387 3388 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 3389 ConstantRange X = getSignedRange(Trunc->getOperand()); 3390 return setSignedRange(Trunc, 3391 ConservativeResult.intersectWith(X.truncate(BitWidth))); 3392 } 3393 3394 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 3395 // If there's no signed wrap, and all the operands have the same sign or 3396 // zero, the value won't ever change sign. 3397 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) { 3398 bool AllNonNeg = true; 3399 bool AllNonPos = true; 3400 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 3401 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false; 3402 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false; 3403 } 3404 if (AllNonNeg) 3405 ConservativeResult = ConservativeResult.intersectWith( 3406 ConstantRange(APInt(BitWidth, 0), 3407 APInt::getSignedMinValue(BitWidth))); 3408 else if (AllNonPos) 3409 ConservativeResult = ConservativeResult.intersectWith( 3410 ConstantRange(APInt::getSignedMinValue(BitWidth), 3411 APInt(BitWidth, 1))); 3412 } 3413 3414 // TODO: non-affine addrec 3415 if (AddRec->isAffine()) { 3416 Type *Ty = AddRec->getType(); 3417 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3418 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3419 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3420 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3421 3422 const SCEV *Start = AddRec->getStart(); 3423 const SCEV *Step = AddRec->getStepRecurrence(*this); 3424 3425 ConstantRange StartRange = getSignedRange(Start); 3426 ConstantRange StepRange = getSignedRange(Step); 3427 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); 3428 ConstantRange EndRange = 3429 StartRange.add(MaxBECountRange.multiply(StepRange)); 3430 3431 // Check for overflow. This must be done with ConstantRange arithmetic 3432 // because we could be called from within the ScalarEvolution overflow 3433 // checking code. 3434 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1); 3435 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1); 3436 ConstantRange ExtMaxBECountRange = 3437 MaxBECountRange.zextOrTrunc(BitWidth*2+1); 3438 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1); 3439 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) != 3440 ExtEndRange) 3441 return setSignedRange(AddRec, ConservativeResult); 3442 3443 APInt Min = APIntOps::smin(StartRange.getSignedMin(), 3444 EndRange.getSignedMin()); 3445 APInt Max = APIntOps::smax(StartRange.getSignedMax(), 3446 EndRange.getSignedMax()); 3447 if (Min.isMinSignedValue() && Max.isMaxSignedValue()) 3448 return setSignedRange(AddRec, ConservativeResult); 3449 return setSignedRange(AddRec, 3450 ConservativeResult.intersectWith(ConstantRange(Min, Max+1))); 3451 } 3452 } 3453 3454 return setSignedRange(AddRec, ConservativeResult); 3455 } 3456 3457 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3458 // For a SCEVUnknown, ask ValueTracking. 3459 if (!U->getValue()->getType()->isIntegerTy() && !TD) 3460 return setSignedRange(U, ConservativeResult); 3461 unsigned NS = ComputeNumSignBits(U->getValue(), TD); 3462 if (NS == 1) 3463 return setSignedRange(U, ConservativeResult); 3464 return setSignedRange(U, ConservativeResult.intersectWith( 3465 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1), 3466 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1))); 3467 } 3468 3469 return setSignedRange(S, ConservativeResult); 3470} 3471 3472/// createSCEV - We know that there is no SCEV for the specified value. 3473/// Analyze the expression. 3474/// 3475const SCEV *ScalarEvolution::createSCEV(Value *V) { 3476 if (!isSCEVable(V->getType())) 3477 return getUnknown(V); 3478 3479 unsigned Opcode = Instruction::UserOp1; 3480 if (Instruction *I = dyn_cast<Instruction>(V)) { 3481 Opcode = I->getOpcode(); 3482 3483 // Don't attempt to analyze instructions in blocks that aren't 3484 // reachable. Such instructions don't matter, and they aren't required 3485 // to obey basic rules for definitions dominating uses which this 3486 // analysis depends on. 3487 if (!DT->isReachableFromEntry(I->getParent())) 3488 return getUnknown(V); 3489 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 3490 Opcode = CE->getOpcode(); 3491 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 3492 return getConstant(CI); 3493 else if (isa<ConstantPointerNull>(V)) 3494 return getConstant(V->getType(), 0); 3495 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) 3496 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee()); 3497 else 3498 return getUnknown(V); 3499 3500 Operator *U = cast<Operator>(V); 3501 switch (Opcode) { 3502 case Instruction::Add: { 3503 // The simple thing to do would be to just call getSCEV on both operands 3504 // and call getAddExpr with the result. However if we're looking at a 3505 // bunch of things all added together, this can be quite inefficient, 3506 // because it leads to N-1 getAddExpr calls for N ultimate operands. 3507 // Instead, gather up all the operands and make a single getAddExpr call. 3508 // LLVM IR canonical form means we need only traverse the left operands. 3509 SmallVector<const SCEV *, 4> AddOps; 3510 AddOps.push_back(getSCEV(U->getOperand(1))); 3511 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) { 3512 unsigned Opcode = Op->getValueID() - Value::InstructionVal; 3513 if (Opcode != Instruction::Add && Opcode != Instruction::Sub) 3514 break; 3515 U = cast<Operator>(Op); 3516 const SCEV *Op1 = getSCEV(U->getOperand(1)); 3517 if (Opcode == Instruction::Sub) 3518 AddOps.push_back(getNegativeSCEV(Op1)); 3519 else 3520 AddOps.push_back(Op1); 3521 } 3522 AddOps.push_back(getSCEV(U->getOperand(0))); 3523 return getAddExpr(AddOps); 3524 } 3525 case Instruction::Mul: { 3526 // See the Add code above. 3527 SmallVector<const SCEV *, 4> MulOps; 3528 MulOps.push_back(getSCEV(U->getOperand(1))); 3529 for (Value *Op = U->getOperand(0); 3530 Op->getValueID() == Instruction::Mul + Value::InstructionVal; 3531 Op = U->getOperand(0)) { 3532 U = cast<Operator>(Op); 3533 MulOps.push_back(getSCEV(U->getOperand(1))); 3534 } 3535 MulOps.push_back(getSCEV(U->getOperand(0))); 3536 return getMulExpr(MulOps); 3537 } 3538 case Instruction::UDiv: 3539 return getUDivExpr(getSCEV(U->getOperand(0)), 3540 getSCEV(U->getOperand(1))); 3541 case Instruction::Sub: 3542 return getMinusSCEV(getSCEV(U->getOperand(0)), 3543 getSCEV(U->getOperand(1))); 3544 case Instruction::And: 3545 // For an expression like x&255 that merely masks off the high bits, 3546 // use zext(trunc(x)) as the SCEV expression. 3547 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3548 if (CI->isNullValue()) 3549 return getSCEV(U->getOperand(1)); 3550 if (CI->isAllOnesValue()) 3551 return getSCEV(U->getOperand(0)); 3552 const APInt &A = CI->getValue(); 3553 3554 // Instcombine's ShrinkDemandedConstant may strip bits out of 3555 // constants, obscuring what would otherwise be a low-bits mask. 3556 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant 3557 // knew about to reconstruct a low-bits mask value. 3558 unsigned LZ = A.countLeadingZeros(); 3559 unsigned BitWidth = A.getBitWidth(); 3560 APInt AllOnes = APInt::getAllOnesValue(BitWidth); 3561 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0); 3562 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD); 3563 3564 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ); 3565 3566 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask)) 3567 return 3568 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), 3569 IntegerType::get(getContext(), BitWidth - LZ)), 3570 U->getType()); 3571 } 3572 break; 3573 3574 case Instruction::Or: 3575 // If the RHS of the Or is a constant, we may have something like: 3576 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 3577 // optimizations will transparently handle this case. 3578 // 3579 // In order for this transformation to be safe, the LHS must be of the 3580 // form X*(2^n) and the Or constant must be less than 2^n. 3581 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3582 const SCEV *LHS = getSCEV(U->getOperand(0)); 3583 const APInt &CIVal = CI->getValue(); 3584 if (GetMinTrailingZeros(LHS) >= 3585 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) { 3586 // Build a plain add SCEV. 3587 const SCEV *S = getAddExpr(LHS, getSCEV(CI)); 3588 // If the LHS of the add was an addrec and it has no-wrap flags, 3589 // transfer the no-wrap flags, since an or won't introduce a wrap. 3590 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) { 3591 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS); 3592 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags( 3593 OldAR->getNoWrapFlags()); 3594 } 3595 return S; 3596 } 3597 } 3598 break; 3599 case Instruction::Xor: 3600 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3601 // If the RHS of the xor is a signbit, then this is just an add. 3602 // Instcombine turns add of signbit into xor as a strength reduction step. 3603 if (CI->getValue().isSignBit()) 3604 return getAddExpr(getSCEV(U->getOperand(0)), 3605 getSCEV(U->getOperand(1))); 3606 3607 // If the RHS of xor is -1, then this is a not operation. 3608 if (CI->isAllOnesValue()) 3609 return getNotSCEV(getSCEV(U->getOperand(0))); 3610 3611 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask. 3612 // This is a variant of the check for xor with -1, and it handles 3613 // the case where instcombine has trimmed non-demanded bits out 3614 // of an xor with -1. 3615 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0))) 3616 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1))) 3617 if (BO->getOpcode() == Instruction::And && 3618 LCI->getValue() == CI->getValue()) 3619 if (const SCEVZeroExtendExpr *Z = 3620 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) { 3621 Type *UTy = U->getType(); 3622 const SCEV *Z0 = Z->getOperand(); 3623 Type *Z0Ty = Z0->getType(); 3624 unsigned Z0TySize = getTypeSizeInBits(Z0Ty); 3625 3626 // If C is a low-bits mask, the zero extend is serving to 3627 // mask off the high bits. Complement the operand and 3628 // re-apply the zext. 3629 if (APIntOps::isMask(Z0TySize, CI->getValue())) 3630 return getZeroExtendExpr(getNotSCEV(Z0), UTy); 3631 3632 // If C is a single bit, it may be in the sign-bit position 3633 // before the zero-extend. In this case, represent the xor 3634 // using an add, which is equivalent, and re-apply the zext. 3635 APInt Trunc = CI->getValue().trunc(Z0TySize); 3636 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() && 3637 Trunc.isSignBit()) 3638 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)), 3639 UTy); 3640 } 3641 } 3642 break; 3643 3644 case Instruction::Shl: 3645 // Turn shift left of a constant amount into a multiply. 3646 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3647 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3648 3649 // If the shift count is not less than the bitwidth, the result of 3650 // the shift is undefined. Don't try to analyze it, because the 3651 // resolution chosen here may differ from the resolution chosen in 3652 // other parts of the compiler. 3653 if (SA->getValue().uge(BitWidth)) 3654 break; 3655 3656 Constant *X = ConstantInt::get(getContext(), 3657 APInt(BitWidth, 1).shl(SA->getZExtValue())); 3658 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3659 } 3660 break; 3661 3662 case Instruction::LShr: 3663 // Turn logical shift right of a constant into a unsigned divide. 3664 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3665 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3666 3667 // If the shift count is not less than the bitwidth, the result of 3668 // the shift is undefined. Don't try to analyze it, because the 3669 // resolution chosen here may differ from the resolution chosen in 3670 // other parts of the compiler. 3671 if (SA->getValue().uge(BitWidth)) 3672 break; 3673 3674 Constant *X = ConstantInt::get(getContext(), 3675 APInt(BitWidth, 1).shl(SA->getZExtValue())); 3676 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3677 } 3678 break; 3679 3680 case Instruction::AShr: 3681 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 3682 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 3683 if (Operator *L = dyn_cast<Operator>(U->getOperand(0))) 3684 if (L->getOpcode() == Instruction::Shl && 3685 L->getOperand(1) == U->getOperand(1)) { 3686 uint64_t BitWidth = getTypeSizeInBits(U->getType()); 3687 3688 // If the shift count is not less than the bitwidth, the result of 3689 // the shift is undefined. Don't try to analyze it, because the 3690 // resolution chosen here may differ from the resolution chosen in 3691 // other parts of the compiler. 3692 if (CI->getValue().uge(BitWidth)) 3693 break; 3694 3695 uint64_t Amt = BitWidth - CI->getZExtValue(); 3696 if (Amt == BitWidth) 3697 return getSCEV(L->getOperand(0)); // shift by zero --> noop 3698 return 3699 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 3700 IntegerType::get(getContext(), 3701 Amt)), 3702 U->getType()); 3703 } 3704 break; 3705 3706 case Instruction::Trunc: 3707 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 3708 3709 case Instruction::ZExt: 3710 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3711 3712 case Instruction::SExt: 3713 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3714 3715 case Instruction::BitCast: 3716 // BitCasts are no-op casts so we just eliminate the cast. 3717 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 3718 return getSCEV(U->getOperand(0)); 3719 break; 3720 3721 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can 3722 // lead to pointer expressions which cannot safely be expanded to GEPs, 3723 // because ScalarEvolution doesn't respect the GEP aliasing rules when 3724 // simplifying integer expressions. 3725 3726 case Instruction::GetElementPtr: 3727 return createNodeForGEP(cast<GEPOperator>(U)); 3728 3729 case Instruction::PHI: 3730 return createNodeForPHI(cast<PHINode>(U)); 3731 3732 case Instruction::Select: 3733 // This could be a smax or umax that was lowered earlier. 3734 // Try to recover it. 3735 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 3736 Value *LHS = ICI->getOperand(0); 3737 Value *RHS = ICI->getOperand(1); 3738 switch (ICI->getPredicate()) { 3739 case ICmpInst::ICMP_SLT: 3740 case ICmpInst::ICMP_SLE: 3741 std::swap(LHS, RHS); 3742 // fall through 3743 case ICmpInst::ICMP_SGT: 3744 case ICmpInst::ICMP_SGE: 3745 // a >s b ? a+x : b+x -> smax(a, b)+x 3746 // a >s b ? b+x : a+x -> smin(a, b)+x 3747 if (LHS->getType() == U->getType()) { 3748 const SCEV *LS = getSCEV(LHS); 3749 const SCEV *RS = getSCEV(RHS); 3750 const SCEV *LA = getSCEV(U->getOperand(1)); 3751 const SCEV *RA = getSCEV(U->getOperand(2)); 3752 const SCEV *LDiff = getMinusSCEV(LA, LS); 3753 const SCEV *RDiff = getMinusSCEV(RA, RS); 3754 if (LDiff == RDiff) 3755 return getAddExpr(getSMaxExpr(LS, RS), LDiff); 3756 LDiff = getMinusSCEV(LA, RS); 3757 RDiff = getMinusSCEV(RA, LS); 3758 if (LDiff == RDiff) 3759 return getAddExpr(getSMinExpr(LS, RS), LDiff); 3760 } 3761 break; 3762 case ICmpInst::ICMP_ULT: 3763 case ICmpInst::ICMP_ULE: 3764 std::swap(LHS, RHS); 3765 // fall through 3766 case ICmpInst::ICMP_UGT: 3767 case ICmpInst::ICMP_UGE: 3768 // a >u b ? a+x : b+x -> umax(a, b)+x 3769 // a >u b ? b+x : a+x -> umin(a, b)+x 3770 if (LHS->getType() == U->getType()) { 3771 const SCEV *LS = getSCEV(LHS); 3772 const SCEV *RS = getSCEV(RHS); 3773 const SCEV *LA = getSCEV(U->getOperand(1)); 3774 const SCEV *RA = getSCEV(U->getOperand(2)); 3775 const SCEV *LDiff = getMinusSCEV(LA, LS); 3776 const SCEV *RDiff = getMinusSCEV(RA, RS); 3777 if (LDiff == RDiff) 3778 return getAddExpr(getUMaxExpr(LS, RS), LDiff); 3779 LDiff = getMinusSCEV(LA, RS); 3780 RDiff = getMinusSCEV(RA, LS); 3781 if (LDiff == RDiff) 3782 return getAddExpr(getUMinExpr(LS, RS), LDiff); 3783 } 3784 break; 3785 case ICmpInst::ICMP_NE: 3786 // n != 0 ? n+x : 1+x -> umax(n, 1)+x 3787 if (LHS->getType() == U->getType() && 3788 isa<ConstantInt>(RHS) && 3789 cast<ConstantInt>(RHS)->isZero()) { 3790 const SCEV *One = getConstant(LHS->getType(), 1); 3791 const SCEV *LS = getSCEV(LHS); 3792 const SCEV *LA = getSCEV(U->getOperand(1)); 3793 const SCEV *RA = getSCEV(U->getOperand(2)); 3794 const SCEV *LDiff = getMinusSCEV(LA, LS); 3795 const SCEV *RDiff = getMinusSCEV(RA, One); 3796 if (LDiff == RDiff) 3797 return getAddExpr(getUMaxExpr(One, LS), LDiff); 3798 } 3799 break; 3800 case ICmpInst::ICMP_EQ: 3801 // n == 0 ? 1+x : n+x -> umax(n, 1)+x 3802 if (LHS->getType() == U->getType() && 3803 isa<ConstantInt>(RHS) && 3804 cast<ConstantInt>(RHS)->isZero()) { 3805 const SCEV *One = getConstant(LHS->getType(), 1); 3806 const SCEV *LS = getSCEV(LHS); 3807 const SCEV *LA = getSCEV(U->getOperand(1)); 3808 const SCEV *RA = getSCEV(U->getOperand(2)); 3809 const SCEV *LDiff = getMinusSCEV(LA, One); 3810 const SCEV *RDiff = getMinusSCEV(RA, LS); 3811 if (LDiff == RDiff) 3812 return getAddExpr(getUMaxExpr(One, LS), LDiff); 3813 } 3814 break; 3815 default: 3816 break; 3817 } 3818 } 3819 3820 default: // We cannot analyze this expression. 3821 break; 3822 } 3823 3824 return getUnknown(V); 3825} 3826 3827 3828 3829//===----------------------------------------------------------------------===// 3830// Iteration Count Computation Code 3831// 3832 3833/// getSmallConstantTripCount - Returns the maximum trip count of this loop as a 3834/// normal unsigned value, if possible. Returns 0 if the trip count is unknown 3835/// or not constant. Will also return 0 if the maximum trip count is very large 3836/// (>= 2^32) 3837unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L, 3838 BasicBlock *ExitBlock) { 3839 const SCEVConstant *ExitCount = 3840 dyn_cast<SCEVConstant>(getExitCount(L, ExitBlock)); 3841 if (!ExitCount) 3842 return 0; 3843 3844 ConstantInt *ExitConst = ExitCount->getValue(); 3845 3846 // Guard against huge trip counts. 3847 if (ExitConst->getValue().getActiveBits() > 32) 3848 return 0; 3849 3850 // In case of integer overflow, this returns 0, which is correct. 3851 return ((unsigned)ExitConst->getZExtValue()) + 1; 3852} 3853 3854/// getSmallConstantTripMultiple - Returns the largest constant divisor of the 3855/// trip count of this loop as a normal unsigned value, if possible. This 3856/// means that the actual trip count is always a multiple of the returned 3857/// value (don't forget the trip count could very well be zero as well!). 3858/// 3859/// Returns 1 if the trip count is unknown or not guaranteed to be the 3860/// multiple of a constant (which is also the case if the trip count is simply 3861/// constant, use getSmallConstantTripCount for that case), Will also return 1 3862/// if the trip count is very large (>= 2^32). 3863unsigned ScalarEvolution::getSmallConstantTripMultiple(Loop *L, 3864 BasicBlock *ExitBlock) { 3865 const SCEV *ExitCount = getExitCount(L, ExitBlock); 3866 if (ExitCount == getCouldNotCompute()) 3867 return 1; 3868 3869 // Get the trip count from the BE count by adding 1. 3870 const SCEV *TCMul = getAddExpr(ExitCount, 3871 getConstant(ExitCount->getType(), 1)); 3872 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt 3873 // to factor simple cases. 3874 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul)) 3875 TCMul = Mul->getOperand(0); 3876 3877 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul); 3878 if (!MulC) 3879 return 1; 3880 3881 ConstantInt *Result = MulC->getValue(); 3882 3883 // Guard against huge trip counts. 3884 if (!Result || Result->getValue().getActiveBits() > 32) 3885 return 1; 3886 3887 return (unsigned)Result->getZExtValue(); 3888} 3889 3890// getExitCount - Get the expression for the number of loop iterations for which 3891// this loop is guaranteed not to exit via ExitintBlock. Otherwise return 3892// SCEVCouldNotCompute. 3893const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) { 3894 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this); 3895} 3896 3897/// getBackedgeTakenCount - If the specified loop has a predictable 3898/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 3899/// object. The backedge-taken count is the number of times the loop header 3900/// will be branched to from within the loop. This is one less than the 3901/// trip count of the loop, since it doesn't count the first iteration, 3902/// when the header is branched to from outside the loop. 3903/// 3904/// Note that it is not valid to call this method on a loop without a 3905/// loop-invariant backedge-taken count (see 3906/// hasLoopInvariantBackedgeTakenCount). 3907/// 3908const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 3909 return getBackedgeTakenInfo(L).getExact(this); 3910} 3911 3912/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except 3913/// return the least SCEV value that is known never to be less than the 3914/// actual backedge taken count. 3915const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) { 3916 return getBackedgeTakenInfo(L).getMax(this); 3917} 3918 3919/// PushLoopPHIs - Push PHI nodes in the header of the given loop 3920/// onto the given Worklist. 3921static void 3922PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) { 3923 BasicBlock *Header = L->getHeader(); 3924 3925 // Push all Loop-header PHIs onto the Worklist stack. 3926 for (BasicBlock::iterator I = Header->begin(); 3927 PHINode *PN = dyn_cast<PHINode>(I); ++I) 3928 Worklist.push_back(PN); 3929} 3930 3931const ScalarEvolution::BackedgeTakenInfo & 3932ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { 3933 // Initially insert an invalid entry for this loop. If the insertion 3934 // succeeds, proceed to actually compute a backedge-taken count and 3935 // update the value. The temporary CouldNotCompute value tells SCEV 3936 // code elsewhere that it shouldn't attempt to request a new 3937 // backedge-taken count, which could result in infinite recursion. 3938 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair = 3939 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo())); 3940 if (!Pair.second) 3941 return Pair.first->second; 3942 3943 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it 3944 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result 3945 // must be cleared in this scope. 3946 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L); 3947 3948 if (Result.getExact(this) != getCouldNotCompute()) { 3949 assert(isLoopInvariant(Result.getExact(this), L) && 3950 isLoopInvariant(Result.getMax(this), L) && 3951 "Computed backedge-taken count isn't loop invariant for loop!"); 3952 ++NumTripCountsComputed; 3953 } 3954 else if (Result.getMax(this) == getCouldNotCompute() && 3955 isa<PHINode>(L->getHeader()->begin())) { 3956 // Only count loops that have phi nodes as not being computable. 3957 ++NumTripCountsNotComputed; 3958 } 3959 3960 // Now that we know more about the trip count for this loop, forget any 3961 // existing SCEV values for PHI nodes in this loop since they are only 3962 // conservative estimates made without the benefit of trip count 3963 // information. This is similar to the code in forgetLoop, except that 3964 // it handles SCEVUnknown PHI nodes specially. 3965 if (Result.hasAnyInfo()) { 3966 SmallVector<Instruction *, 16> Worklist; 3967 PushLoopPHIs(L, Worklist); 3968 3969 SmallPtrSet<Instruction *, 8> Visited; 3970 while (!Worklist.empty()) { 3971 Instruction *I = Worklist.pop_back_val(); 3972 if (!Visited.insert(I)) continue; 3973 3974 ValueExprMapType::iterator It = 3975 ValueExprMap.find(static_cast<Value *>(I)); 3976 if (It != ValueExprMap.end()) { 3977 const SCEV *Old = It->second; 3978 3979 // SCEVUnknown for a PHI either means that it has an unrecognized 3980 // structure, or it's a PHI that's in the progress of being computed 3981 // by createNodeForPHI. In the former case, additional loop trip 3982 // count information isn't going to change anything. In the later 3983 // case, createNodeForPHI will perform the necessary updates on its 3984 // own when it gets to that point. 3985 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) { 3986 forgetMemoizedResults(Old); 3987 ValueExprMap.erase(It); 3988 } 3989 if (PHINode *PN = dyn_cast<PHINode>(I)) 3990 ConstantEvolutionLoopExitValue.erase(PN); 3991 } 3992 3993 PushDefUseChildren(I, Worklist); 3994 } 3995 } 3996 3997 // Re-lookup the insert position, since the call to 3998 // ComputeBackedgeTakenCount above could result in a 3999 // recusive call to getBackedgeTakenInfo (on a different 4000 // loop), which would invalidate the iterator computed 4001 // earlier. 4002 return BackedgeTakenCounts.find(L)->second = Result; 4003} 4004 4005/// forgetLoop - This method should be called by the client when it has 4006/// changed a loop in a way that may effect ScalarEvolution's ability to 4007/// compute a trip count, or if the loop is deleted. 4008void ScalarEvolution::forgetLoop(const Loop *L) { 4009 // Drop any stored trip count value. 4010 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos = 4011 BackedgeTakenCounts.find(L); 4012 if (BTCPos != BackedgeTakenCounts.end()) { 4013 BTCPos->second.clear(); 4014 BackedgeTakenCounts.erase(BTCPos); 4015 } 4016 4017 // Drop information about expressions based on loop-header PHIs. 4018 SmallVector<Instruction *, 16> Worklist; 4019 PushLoopPHIs(L, Worklist); 4020 4021 SmallPtrSet<Instruction *, 8> Visited; 4022 while (!Worklist.empty()) { 4023 Instruction *I = Worklist.pop_back_val(); 4024 if (!Visited.insert(I)) continue; 4025 4026 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I)); 4027 if (It != ValueExprMap.end()) { 4028 forgetMemoizedResults(It->second); 4029 ValueExprMap.erase(It); 4030 if (PHINode *PN = dyn_cast<PHINode>(I)) 4031 ConstantEvolutionLoopExitValue.erase(PN); 4032 } 4033 4034 PushDefUseChildren(I, Worklist); 4035 } 4036 4037 // Forget all contained loops too, to avoid dangling entries in the 4038 // ValuesAtScopes map. 4039 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 4040 forgetLoop(*I); 4041} 4042 4043/// forgetValue - This method should be called by the client when it has 4044/// changed a value in a way that may effect its value, or which may 4045/// disconnect it from a def-use chain linking it to a loop. 4046void ScalarEvolution::forgetValue(Value *V) { 4047 Instruction *I = dyn_cast<Instruction>(V); 4048 if (!I) return; 4049 4050 // Drop information about expressions based on loop-header PHIs. 4051 SmallVector<Instruction *, 16> Worklist; 4052 Worklist.push_back(I); 4053 4054 SmallPtrSet<Instruction *, 8> Visited; 4055 while (!Worklist.empty()) { 4056 I = Worklist.pop_back_val(); 4057 if (!Visited.insert(I)) continue; 4058 4059 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I)); 4060 if (It != ValueExprMap.end()) { 4061 forgetMemoizedResults(It->second); 4062 ValueExprMap.erase(It); 4063 if (PHINode *PN = dyn_cast<PHINode>(I)) 4064 ConstantEvolutionLoopExitValue.erase(PN); 4065 } 4066 4067 PushDefUseChildren(I, Worklist); 4068 } 4069} 4070 4071/// getExact - Get the exact loop backedge taken count considering all loop 4072/// exits. If all exits are computable, this is the minimum computed count. 4073const SCEV * 4074ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const { 4075 // If any exits were not computable, the loop is not computable. 4076 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute(); 4077 4078 // We need at least one computable exit. 4079 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute(); 4080 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info"); 4081 4082 const SCEV *BECount = 0; 4083 for (const ExitNotTakenInfo *ENT = &ExitNotTaken; 4084 ENT != 0; ENT = ENT->getNextExit()) { 4085 4086 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV"); 4087 4088 if (!BECount) 4089 BECount = ENT->ExactNotTaken; 4090 else 4091 BECount = SE->getUMinFromMismatchedTypes(BECount, ENT->ExactNotTaken); 4092 } 4093 assert(BECount && "Invalid not taken count for loop exit"); 4094 return BECount; 4095} 4096 4097/// getExact - Get the exact not taken count for this loop exit. 4098const SCEV * 4099ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock, 4100 ScalarEvolution *SE) const { 4101 for (const ExitNotTakenInfo *ENT = &ExitNotTaken; 4102 ENT != 0; ENT = ENT->getNextExit()) { 4103 4104 if (ENT->ExitingBlock == ExitingBlock) 4105 return ENT->ExactNotTaken; 4106 } 4107 return SE->getCouldNotCompute(); 4108} 4109 4110/// getMax - Get the max backedge taken count for the loop. 4111const SCEV * 4112ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const { 4113 return Max ? Max : SE->getCouldNotCompute(); 4114} 4115 4116/// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each 4117/// computable exit into a persistent ExitNotTakenInfo array. 4118ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo( 4119 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts, 4120 bool Complete, const SCEV *MaxCount) : Max(MaxCount) { 4121 4122 if (!Complete) 4123 ExitNotTaken.setIncomplete(); 4124 4125 unsigned NumExits = ExitCounts.size(); 4126 if (NumExits == 0) return; 4127 4128 ExitNotTaken.ExitingBlock = ExitCounts[0].first; 4129 ExitNotTaken.ExactNotTaken = ExitCounts[0].second; 4130 if (NumExits == 1) return; 4131 4132 // Handle the rare case of multiple computable exits. 4133 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1]; 4134 4135 ExitNotTakenInfo *PrevENT = &ExitNotTaken; 4136 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) { 4137 PrevENT->setNextExit(ENT); 4138 ENT->ExitingBlock = ExitCounts[i].first; 4139 ENT->ExactNotTaken = ExitCounts[i].second; 4140 } 4141} 4142 4143/// clear - Invalidate this result and free the ExitNotTakenInfo array. 4144void ScalarEvolution::BackedgeTakenInfo::clear() { 4145 ExitNotTaken.ExitingBlock = 0; 4146 ExitNotTaken.ExactNotTaken = 0; 4147 delete[] ExitNotTaken.getNextExit(); 4148} 4149 4150/// ComputeBackedgeTakenCount - Compute the number of times the backedge 4151/// of the specified loop will execute. 4152ScalarEvolution::BackedgeTakenInfo 4153ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 4154 SmallVector<BasicBlock *, 8> ExitingBlocks; 4155 L->getExitingBlocks(ExitingBlocks); 4156 4157 // Examine all exits and pick the most conservative values. 4158 const SCEV *MaxBECount = getCouldNotCompute(); 4159 bool CouldComputeBECount = true; 4160 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts; 4161 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) { 4162 ExitLimit EL = ComputeExitLimit(L, ExitingBlocks[i]); 4163 if (EL.Exact == getCouldNotCompute()) 4164 // We couldn't compute an exact value for this exit, so 4165 // we won't be able to compute an exact value for the loop. 4166 CouldComputeBECount = false; 4167 else 4168 ExitCounts.push_back(std::make_pair(ExitingBlocks[i], EL.Exact)); 4169 4170 if (MaxBECount == getCouldNotCompute()) 4171 MaxBECount = EL.Max; 4172 else if (EL.Max != getCouldNotCompute()) 4173 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, EL.Max); 4174 } 4175 4176 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount); 4177} 4178 4179/// ComputeExitLimit - Compute the number of times the backedge of the specified 4180/// loop will execute if it exits via the specified block. 4181ScalarEvolution::ExitLimit 4182ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) { 4183 4184 // Okay, we've chosen an exiting block. See what condition causes us to 4185 // exit at this block. 4186 // 4187 // FIXME: we should be able to handle switch instructions (with a single exit) 4188 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 4189 if (ExitBr == 0) return getCouldNotCompute(); 4190 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 4191 4192 // At this point, we know we have a conditional branch that determines whether 4193 // the loop is exited. However, we don't know if the branch is executed each 4194 // time through the loop. If not, then the execution count of the branch will 4195 // not be equal to the trip count of the loop. 4196 // 4197 // Currently we check for this by checking to see if the Exit branch goes to 4198 // the loop header. If so, we know it will always execute the same number of 4199 // times as the loop. We also handle the case where the exit block *is* the 4200 // loop header. This is common for un-rotated loops. 4201 // 4202 // If both of those tests fail, walk up the unique predecessor chain to the 4203 // header, stopping if there is an edge that doesn't exit the loop. If the 4204 // header is reached, the execution count of the branch will be equal to the 4205 // trip count of the loop. 4206 // 4207 // More extensive analysis could be done to handle more cases here. 4208 // 4209 if (ExitBr->getSuccessor(0) != L->getHeader() && 4210 ExitBr->getSuccessor(1) != L->getHeader() && 4211 ExitBr->getParent() != L->getHeader()) { 4212 // The simple checks failed, try climbing the unique predecessor chain 4213 // up to the header. 4214 bool Ok = false; 4215 for (BasicBlock *BB = ExitBr->getParent(); BB; ) { 4216 BasicBlock *Pred = BB->getUniquePredecessor(); 4217 if (!Pred) 4218 return getCouldNotCompute(); 4219 TerminatorInst *PredTerm = Pred->getTerminator(); 4220 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) { 4221 BasicBlock *PredSucc = PredTerm->getSuccessor(i); 4222 if (PredSucc == BB) 4223 continue; 4224 // If the predecessor has a successor that isn't BB and isn't 4225 // outside the loop, assume the worst. 4226 if (L->contains(PredSucc)) 4227 return getCouldNotCompute(); 4228 } 4229 if (Pred == L->getHeader()) { 4230 Ok = true; 4231 break; 4232 } 4233 BB = Pred; 4234 } 4235 if (!Ok) 4236 return getCouldNotCompute(); 4237 } 4238 4239 // Proceed to the next level to examine the exit condition expression. 4240 return ComputeExitLimitFromCond(L, ExitBr->getCondition(), 4241 ExitBr->getSuccessor(0), 4242 ExitBr->getSuccessor(1)); 4243} 4244 4245/// ComputeExitLimitFromCond - Compute the number of times the 4246/// backedge of the specified loop will execute if its exit condition 4247/// were a conditional branch of ExitCond, TBB, and FBB. 4248ScalarEvolution::ExitLimit 4249ScalarEvolution::ComputeExitLimitFromCond(const Loop *L, 4250 Value *ExitCond, 4251 BasicBlock *TBB, 4252 BasicBlock *FBB) { 4253 // Check if the controlling expression for this loop is an And or Or. 4254 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) { 4255 if (BO->getOpcode() == Instruction::And) { 4256 // Recurse on the operands of the and. 4257 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB); 4258 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB); 4259 const SCEV *BECount = getCouldNotCompute(); 4260 const SCEV *MaxBECount = getCouldNotCompute(); 4261 if (L->contains(TBB)) { 4262 // Both conditions must be true for the loop to continue executing. 4263 // Choose the less conservative count. 4264 if (EL0.Exact == getCouldNotCompute() || 4265 EL1.Exact == getCouldNotCompute()) 4266 BECount = getCouldNotCompute(); 4267 else 4268 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact); 4269 if (EL0.Max == getCouldNotCompute()) 4270 MaxBECount = EL1.Max; 4271 else if (EL1.Max == getCouldNotCompute()) 4272 MaxBECount = EL0.Max; 4273 else 4274 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max); 4275 } else { 4276 // Both conditions must be true at the same time for the loop to exit. 4277 // For now, be conservative. 4278 assert(L->contains(FBB) && "Loop block has no successor in loop!"); 4279 if (EL0.Max == EL1.Max) 4280 MaxBECount = EL0.Max; 4281 if (EL0.Exact == EL1.Exact) 4282 BECount = EL0.Exact; 4283 } 4284 4285 return ExitLimit(BECount, MaxBECount); 4286 } 4287 if (BO->getOpcode() == Instruction::Or) { 4288 // Recurse on the operands of the or. 4289 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB); 4290 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB); 4291 const SCEV *BECount = getCouldNotCompute(); 4292 const SCEV *MaxBECount = getCouldNotCompute(); 4293 if (L->contains(FBB)) { 4294 // Both conditions must be false for the loop to continue executing. 4295 // Choose the less conservative count. 4296 if (EL0.Exact == getCouldNotCompute() || 4297 EL1.Exact == getCouldNotCompute()) 4298 BECount = getCouldNotCompute(); 4299 else 4300 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact); 4301 if (EL0.Max == getCouldNotCompute()) 4302 MaxBECount = EL1.Max; 4303 else if (EL1.Max == getCouldNotCompute()) 4304 MaxBECount = EL0.Max; 4305 else 4306 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max); 4307 } else { 4308 // Both conditions must be false at the same time for the loop to exit. 4309 // For now, be conservative. 4310 assert(L->contains(TBB) && "Loop block has no successor in loop!"); 4311 if (EL0.Max == EL1.Max) 4312 MaxBECount = EL0.Max; 4313 if (EL0.Exact == EL1.Exact) 4314 BECount = EL0.Exact; 4315 } 4316 4317 return ExitLimit(BECount, MaxBECount); 4318 } 4319 } 4320 4321 // With an icmp, it may be feasible to compute an exact backedge-taken count. 4322 // Proceed to the next level to examine the icmp. 4323 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) 4324 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB); 4325 4326 // Check for a constant condition. These are normally stripped out by 4327 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to 4328 // preserve the CFG and is temporarily leaving constant conditions 4329 // in place. 4330 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) { 4331 if (L->contains(FBB) == !CI->getZExtValue()) 4332 // The backedge is always taken. 4333 return getCouldNotCompute(); 4334 else 4335 // The backedge is never taken. 4336 return getConstant(CI->getType(), 0); 4337 } 4338 4339 // If it's not an integer or pointer comparison then compute it the hard way. 4340 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB)); 4341} 4342 4343/// ComputeExitLimitFromICmp - Compute the number of times the 4344/// backedge of the specified loop will execute if its exit condition 4345/// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB. 4346ScalarEvolution::ExitLimit 4347ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L, 4348 ICmpInst *ExitCond, 4349 BasicBlock *TBB, 4350 BasicBlock *FBB) { 4351 4352 // If the condition was exit on true, convert the condition to exit on false 4353 ICmpInst::Predicate Cond; 4354 if (!L->contains(FBB)) 4355 Cond = ExitCond->getPredicate(); 4356 else 4357 Cond = ExitCond->getInversePredicate(); 4358 4359 // Handle common loops like: for (X = "string"; *X; ++X) 4360 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 4361 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 4362 ExitLimit ItCnt = 4363 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond); 4364 if (ItCnt.hasAnyInfo()) 4365 return ItCnt; 4366 } 4367 4368 const SCEV *LHS = getSCEV(ExitCond->getOperand(0)); 4369 const SCEV *RHS = getSCEV(ExitCond->getOperand(1)); 4370 4371 // Try to evaluate any dependencies out of the loop. 4372 LHS = getSCEVAtScope(LHS, L); 4373 RHS = getSCEVAtScope(RHS, L); 4374 4375 // At this point, we would like to compute how many iterations of the 4376 // loop the predicate will return true for these inputs. 4377 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) { 4378 // If there is a loop-invariant, force it into the RHS. 4379 std::swap(LHS, RHS); 4380 Cond = ICmpInst::getSwappedPredicate(Cond); 4381 } 4382 4383 // Simplify the operands before analyzing them. 4384 (void)SimplifyICmpOperands(Cond, LHS, RHS); 4385 4386 // If we have a comparison of a chrec against a constant, try to use value 4387 // ranges to answer this query. 4388 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 4389 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 4390 if (AddRec->getLoop() == L) { 4391 // Form the constant range. 4392 ConstantRange CompRange( 4393 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue())); 4394 4395 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this); 4396 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 4397 } 4398 4399 switch (Cond) { 4400 case ICmpInst::ICMP_NE: { // while (X != Y) 4401 // Convert to: while (X-Y != 0) 4402 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L); 4403 if (EL.hasAnyInfo()) return EL; 4404 break; 4405 } 4406 case ICmpInst::ICMP_EQ: { // while (X == Y) 4407 // Convert to: while (X-Y == 0) 4408 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 4409 if (EL.hasAnyInfo()) return EL; 4410 break; 4411 } 4412 case ICmpInst::ICMP_SLT: { 4413 ExitLimit EL = HowManyLessThans(LHS, RHS, L, true); 4414 if (EL.hasAnyInfo()) return EL; 4415 break; 4416 } 4417 case ICmpInst::ICMP_SGT: { 4418 ExitLimit EL = HowManyLessThans(getNotSCEV(LHS), 4419 getNotSCEV(RHS), L, true); 4420 if (EL.hasAnyInfo()) return EL; 4421 break; 4422 } 4423 case ICmpInst::ICMP_ULT: { 4424 ExitLimit EL = HowManyLessThans(LHS, RHS, L, false); 4425 if (EL.hasAnyInfo()) return EL; 4426 break; 4427 } 4428 case ICmpInst::ICMP_UGT: { 4429 ExitLimit EL = HowManyLessThans(getNotSCEV(LHS), 4430 getNotSCEV(RHS), L, false); 4431 if (EL.hasAnyInfo()) return EL; 4432 break; 4433 } 4434 default: 4435#if 0 4436 dbgs() << "ComputeBackedgeTakenCount "; 4437 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 4438 dbgs() << "[unsigned] "; 4439 dbgs() << *LHS << " " 4440 << Instruction::getOpcodeName(Instruction::ICmp) 4441 << " " << *RHS << "\n"; 4442#endif 4443 break; 4444 } 4445 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB)); 4446} 4447 4448static ConstantInt * 4449EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 4450 ScalarEvolution &SE) { 4451 const SCEV *InVal = SE.getConstant(C); 4452 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE); 4453 assert(isa<SCEVConstant>(Val) && 4454 "Evaluation of SCEV at constant didn't fold correctly?"); 4455 return cast<SCEVConstant>(Val)->getValue(); 4456} 4457 4458/// GetAddressedElementFromGlobal - Given a global variable with an initializer 4459/// and a GEP expression (missing the pointer index) indexing into it, return 4460/// the addressed element of the initializer or null if the index expression is 4461/// invalid. 4462static Constant * 4463GetAddressedElementFromGlobal(GlobalVariable *GV, 4464 const std::vector<ConstantInt*> &Indices) { 4465 Constant *Init = GV->getInitializer(); 4466 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 4467 uint64_t Idx = Indices[i]->getZExtValue(); 4468 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 4469 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 4470 Init = cast<Constant>(CS->getOperand(Idx)); 4471 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 4472 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 4473 Init = cast<Constant>(CA->getOperand(Idx)); 4474 } else if (isa<ConstantAggregateZero>(Init)) { 4475 if (StructType *STy = dyn_cast<StructType>(Init->getType())) { 4476 assert(Idx < STy->getNumElements() && "Bad struct index!"); 4477 Init = Constant::getNullValue(STy->getElementType(Idx)); 4478 } else if (ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 4479 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 4480 Init = Constant::getNullValue(ATy->getElementType()); 4481 } else { 4482 llvm_unreachable("Unknown constant aggregate type!"); 4483 } 4484 return 0; 4485 } else { 4486 return 0; // Unknown initializer type 4487 } 4488 } 4489 return Init; 4490} 4491 4492/// ComputeLoadConstantCompareExitLimit - Given an exit condition of 4493/// 'icmp op load X, cst', try to see if we can compute the backedge 4494/// execution count. 4495ScalarEvolution::ExitLimit 4496ScalarEvolution::ComputeLoadConstantCompareExitLimit( 4497 LoadInst *LI, 4498 Constant *RHS, 4499 const Loop *L, 4500 ICmpInst::Predicate predicate) { 4501 4502 if (LI->isVolatile()) return getCouldNotCompute(); 4503 4504 // Check to see if the loaded pointer is a getelementptr of a global. 4505 // TODO: Use SCEV instead of manually grubbing with GEPs. 4506 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 4507 if (!GEP) return getCouldNotCompute(); 4508 4509 // Make sure that it is really a constant global we are gepping, with an 4510 // initializer, and make sure the first IDX is really 0. 4511 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 4512 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() || 4513 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 4514 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 4515 return getCouldNotCompute(); 4516 4517 // Okay, we allow one non-constant index into the GEP instruction. 4518 Value *VarIdx = 0; 4519 std::vector<ConstantInt*> Indexes; 4520 unsigned VarIdxNum = 0; 4521 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 4522 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 4523 Indexes.push_back(CI); 4524 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 4525 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's. 4526 VarIdx = GEP->getOperand(i); 4527 VarIdxNum = i-2; 4528 Indexes.push_back(0); 4529 } 4530 4531 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 4532 // Check to see if X is a loop variant variable value now. 4533 const SCEV *Idx = getSCEV(VarIdx); 4534 Idx = getSCEVAtScope(Idx, L); 4535 4536 // We can only recognize very limited forms of loop index expressions, in 4537 // particular, only affine AddRec's like {C1,+,C2}. 4538 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 4539 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) || 4540 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 4541 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 4542 return getCouldNotCompute(); 4543 4544 unsigned MaxSteps = MaxBruteForceIterations; 4545 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 4546 ConstantInt *ItCst = ConstantInt::get( 4547 cast<IntegerType>(IdxExpr->getType()), IterationNum); 4548 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 4549 4550 // Form the GEP offset. 4551 Indexes[VarIdxNum] = Val; 4552 4553 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 4554 if (Result == 0) break; // Cannot compute! 4555 4556 // Evaluate the condition for this iteration. 4557 Result = ConstantExpr::getICmp(predicate, Result, RHS); 4558 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 4559 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 4560#if 0 4561 dbgs() << "\n***\n*** Computed loop count " << *ItCst 4562 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 4563 << "***\n"; 4564#endif 4565 ++NumArrayLenItCounts; 4566 return getConstant(ItCst); // Found terminating iteration! 4567 } 4568 } 4569 return getCouldNotCompute(); 4570} 4571 4572 4573/// CanConstantFold - Return true if we can constant fold an instruction of the 4574/// specified type, assuming that all operands were constants. 4575static bool CanConstantFold(const Instruction *I) { 4576 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 4577 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 4578 return true; 4579 4580 if (const CallInst *CI = dyn_cast<CallInst>(I)) 4581 if (const Function *F = CI->getCalledFunction()) 4582 return canConstantFoldCallTo(F); 4583 return false; 4584} 4585 4586/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 4587/// in the loop that V is derived from. We allow arbitrary operations along the 4588/// way, but the operands of an operation must either be constants or a value 4589/// derived from a constant PHI. If this expression does not fit with these 4590/// constraints, return null. 4591static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 4592 // If this is not an instruction, or if this is an instruction outside of the 4593 // loop, it can't be derived from a loop PHI. 4594 Instruction *I = dyn_cast<Instruction>(V); 4595 if (I == 0 || !L->contains(I)) return 0; 4596 4597 if (PHINode *PN = dyn_cast<PHINode>(I)) { 4598 if (L->getHeader() == I->getParent()) 4599 return PN; 4600 else 4601 // We don't currently keep track of the control flow needed to evaluate 4602 // PHIs, so we cannot handle PHIs inside of loops. 4603 return 0; 4604 } 4605 4606 // If we won't be able to constant fold this expression even if the operands 4607 // are constants, return early. 4608 if (!CanConstantFold(I)) return 0; 4609 4610 // Otherwise, we can evaluate this instruction if all of its operands are 4611 // constant or derived from a PHI node themselves. 4612 PHINode *PHI = 0; 4613 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 4614 if (!isa<Constant>(I->getOperand(Op))) { 4615 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 4616 if (P == 0) return 0; // Not evolving from PHI 4617 if (PHI == 0) 4618 PHI = P; 4619 else if (PHI != P) 4620 return 0; // Evolving from multiple different PHIs. 4621 } 4622 4623 // This is a expression evolving from a constant PHI! 4624 return PHI; 4625} 4626 4627/// EvaluateExpression - Given an expression that passes the 4628/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 4629/// in the loop has the value PHIVal. If we can't fold this expression for some 4630/// reason, return null. 4631static Constant *EvaluateExpression(Value *V, Constant *PHIVal, 4632 const TargetData *TD) { 4633 if (isa<PHINode>(V)) return PHIVal; 4634 if (Constant *C = dyn_cast<Constant>(V)) return C; 4635 Instruction *I = cast<Instruction>(V); 4636 4637 std::vector<Constant*> Operands(I->getNumOperands()); 4638 4639 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4640 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD); 4641 if (Operands[i] == 0) return 0; 4642 } 4643 4644 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4645 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0], 4646 Operands[1], TD); 4647 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, TD); 4648} 4649 4650/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 4651/// in the header of its containing loop, we know the loop executes a 4652/// constant number of times, and the PHI node is just a recurrence 4653/// involving constants, fold it. 4654Constant * 4655ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN, 4656 const APInt &BEs, 4657 const Loop *L) { 4658 DenseMap<PHINode*, Constant*>::const_iterator I = 4659 ConstantEvolutionLoopExitValue.find(PN); 4660 if (I != ConstantEvolutionLoopExitValue.end()) 4661 return I->second; 4662 4663 if (BEs.ugt(MaxBruteForceIterations)) 4664 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 4665 4666 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 4667 4668 // Since the loop is canonicalized, the PHI node must have two entries. One 4669 // entry must be a constant (coming in from outside of the loop), and the 4670 // second must be derived from the same PHI. 4671 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4672 Constant *StartCST = 4673 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4674 if (StartCST == 0) 4675 return RetVal = 0; // Must be a constant. 4676 4677 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4678 if (getConstantEvolvingPHI(BEValue, L) != PN && 4679 !isa<Constant>(BEValue)) 4680 return RetVal = 0; // Not derived from same PHI. 4681 4682 // Execute the loop symbolically to determine the exit value. 4683 if (BEs.getActiveBits() >= 32) 4684 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 4685 4686 unsigned NumIterations = BEs.getZExtValue(); // must be in range 4687 unsigned IterationNum = 0; 4688 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 4689 if (IterationNum == NumIterations) 4690 return RetVal = PHIVal; // Got exit value! 4691 4692 // Compute the value of the PHI node for the next iteration. 4693 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4694 if (NextPHI == PHIVal) 4695 return RetVal = NextPHI; // Stopped evolving! 4696 if (NextPHI == 0) 4697 return 0; // Couldn't evaluate! 4698 PHIVal = NextPHI; 4699 } 4700} 4701 4702/// ComputeExitCountExhaustively - If the loop is known to execute a 4703/// constant number of times (the condition evolves only from constants), 4704/// try to evaluate a few iterations of the loop until we get the exit 4705/// condition gets a value of ExitWhen (true or false). If we cannot 4706/// evaluate the trip count of the loop, return getCouldNotCompute(). 4707const SCEV * ScalarEvolution::ComputeExitCountExhaustively(const Loop *L, 4708 Value *Cond, 4709 bool ExitWhen) { 4710 PHINode *PN = getConstantEvolvingPHI(Cond, L); 4711 if (PN == 0) return getCouldNotCompute(); 4712 4713 // If the loop is canonicalized, the PHI will have exactly two entries. 4714 // That's the only form we support here. 4715 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute(); 4716 4717 // One entry must be a constant (coming in from outside of the loop), and the 4718 // second must be derived from the same PHI. 4719 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4720 Constant *StartCST = 4721 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4722 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant. 4723 4724 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4725 if (getConstantEvolvingPHI(BEValue, L) != PN && 4726 !isa<Constant>(BEValue)) 4727 return getCouldNotCompute(); // Not derived from same PHI. 4728 4729 // Okay, we find a PHI node that defines the trip count of this loop. Execute 4730 // the loop symbolically to determine when the condition gets a value of 4731 // "ExitWhen". 4732 unsigned IterationNum = 0; 4733 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 4734 for (Constant *PHIVal = StartCST; 4735 IterationNum != MaxIterations; ++IterationNum) { 4736 ConstantInt *CondVal = 4737 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD)); 4738 4739 // Couldn't symbolically evaluate. 4740 if (!CondVal) return getCouldNotCompute(); 4741 4742 if (CondVal->getValue() == uint64_t(ExitWhen)) { 4743 ++NumBruteForceTripCountsComputed; 4744 return getConstant(Type::getInt32Ty(getContext()), IterationNum); 4745 } 4746 4747 // Compute the value of the PHI node for the next iteration. 4748 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4749 if (NextPHI == 0 || NextPHI == PHIVal) 4750 return getCouldNotCompute();// Couldn't evaluate or not making progress... 4751 PHIVal = NextPHI; 4752 } 4753 4754 // Too many iterations were needed to evaluate. 4755 return getCouldNotCompute(); 4756} 4757 4758/// getSCEVAtScope - Return a SCEV expression for the specified value 4759/// at the specified scope in the program. The L value specifies a loop 4760/// nest to evaluate the expression at, where null is the top-level or a 4761/// specified loop is immediately inside of the loop. 4762/// 4763/// This method can be used to compute the exit value for a variable defined 4764/// in a loop by querying what the value will hold in the parent loop. 4765/// 4766/// In the case that a relevant loop exit value cannot be computed, the 4767/// original value V is returned. 4768const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { 4769 // Check to see if we've folded this expression at this loop before. 4770 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V]; 4771 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair = 4772 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0))); 4773 if (!Pair.second) 4774 return Pair.first->second ? Pair.first->second : V; 4775 4776 // Otherwise compute it. 4777 const SCEV *C = computeSCEVAtScope(V, L); 4778 ValuesAtScopes[V][L] = C; 4779 return C; 4780} 4781 4782const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) { 4783 if (isa<SCEVConstant>(V)) return V; 4784 4785 // If this instruction is evolved from a constant-evolving PHI, compute the 4786 // exit value from the loop without using SCEVs. 4787 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 4788 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 4789 const Loop *LI = (*this->LI)[I->getParent()]; 4790 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 4791 if (PHINode *PN = dyn_cast<PHINode>(I)) 4792 if (PN->getParent() == LI->getHeader()) { 4793 // Okay, there is no closed form solution for the PHI node. Check 4794 // to see if the loop that contains it has a known backedge-taken 4795 // count. If so, we may be able to force computation of the exit 4796 // value. 4797 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI); 4798 if (const SCEVConstant *BTCC = 4799 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 4800 // Okay, we know how many times the containing loop executes. If 4801 // this is a constant evolving PHI node, get the final value at 4802 // the specified iteration number. 4803 Constant *RV = getConstantEvolutionLoopExitValue(PN, 4804 BTCC->getValue()->getValue(), 4805 LI); 4806 if (RV) return getSCEV(RV); 4807 } 4808 } 4809 4810 // Okay, this is an expression that we cannot symbolically evaluate 4811 // into a SCEV. Check to see if it's possible to symbolically evaluate 4812 // the arguments into constants, and if so, try to constant propagate the 4813 // result. This is particularly useful for computing loop exit values. 4814 if (CanConstantFold(I)) { 4815 SmallVector<Constant *, 4> Operands; 4816 bool MadeImprovement = false; 4817 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4818 Value *Op = I->getOperand(i); 4819 if (Constant *C = dyn_cast<Constant>(Op)) { 4820 Operands.push_back(C); 4821 continue; 4822 } 4823 4824 // If any of the operands is non-constant and if they are 4825 // non-integer and non-pointer, don't even try to analyze them 4826 // with scev techniques. 4827 if (!isSCEVable(Op->getType())) 4828 return V; 4829 4830 const SCEV *OrigV = getSCEV(Op); 4831 const SCEV *OpV = getSCEVAtScope(OrigV, L); 4832 MadeImprovement |= OrigV != OpV; 4833 4834 Constant *C = 0; 4835 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 4836 C = SC->getValue(); 4837 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) 4838 C = dyn_cast<Constant>(SU->getValue()); 4839 if (!C) return V; 4840 if (C->getType() != Op->getType()) 4841 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 4842 Op->getType(), 4843 false), 4844 C, Op->getType()); 4845 Operands.push_back(C); 4846 } 4847 4848 // Check to see if getSCEVAtScope actually made an improvement. 4849 if (MadeImprovement) { 4850 Constant *C = 0; 4851 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4852 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 4853 Operands[0], Operands[1], TD); 4854 else 4855 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 4856 Operands, TD); 4857 if (!C) return V; 4858 return getSCEV(C); 4859 } 4860 } 4861 } 4862 4863 // This is some other type of SCEVUnknown, just return it. 4864 return V; 4865 } 4866 4867 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 4868 // Avoid performing the look-up in the common case where the specified 4869 // expression has no loop-variant portions. 4870 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 4871 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4872 if (OpAtScope != Comm->getOperand(i)) { 4873 // Okay, at least one of these operands is loop variant but might be 4874 // foldable. Build a new instance of the folded commutative expression. 4875 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(), 4876 Comm->op_begin()+i); 4877 NewOps.push_back(OpAtScope); 4878 4879 for (++i; i != e; ++i) { 4880 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4881 NewOps.push_back(OpAtScope); 4882 } 4883 if (isa<SCEVAddExpr>(Comm)) 4884 return getAddExpr(NewOps); 4885 if (isa<SCEVMulExpr>(Comm)) 4886 return getMulExpr(NewOps); 4887 if (isa<SCEVSMaxExpr>(Comm)) 4888 return getSMaxExpr(NewOps); 4889 if (isa<SCEVUMaxExpr>(Comm)) 4890 return getUMaxExpr(NewOps); 4891 llvm_unreachable("Unknown commutative SCEV type!"); 4892 } 4893 } 4894 // If we got here, all operands are loop invariant. 4895 return Comm; 4896 } 4897 4898 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 4899 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L); 4900 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L); 4901 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 4902 return Div; // must be loop invariant 4903 return getUDivExpr(LHS, RHS); 4904 } 4905 4906 // If this is a loop recurrence for a loop that does not contain L, then we 4907 // are dealing with the final value computed by the loop. 4908 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 4909 // First, attempt to evaluate each operand. 4910 // Avoid performing the look-up in the common case where the specified 4911 // expression has no loop-variant portions. 4912 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 4913 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L); 4914 if (OpAtScope == AddRec->getOperand(i)) 4915 continue; 4916 4917 // Okay, at least one of these operands is loop variant but might be 4918 // foldable. Build a new instance of the folded commutative expression. 4919 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(), 4920 AddRec->op_begin()+i); 4921 NewOps.push_back(OpAtScope); 4922 for (++i; i != e; ++i) 4923 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L)); 4924 4925 const SCEV *FoldedRec = 4926 getAddRecExpr(NewOps, AddRec->getLoop(), 4927 AddRec->getNoWrapFlags(SCEV::FlagNW)); 4928 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec); 4929 // The addrec may be folded to a nonrecurrence, for example, if the 4930 // induction variable is multiplied by zero after constant folding. Go 4931 // ahead and return the folded value. 4932 if (!AddRec) 4933 return FoldedRec; 4934 break; 4935 } 4936 4937 // If the scope is outside the addrec's loop, evaluate it by using the 4938 // loop exit value of the addrec. 4939 if (!AddRec->getLoop()->contains(L)) { 4940 // To evaluate this recurrence, we need to know how many times the AddRec 4941 // loop iterates. Compute this now. 4942 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 4943 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec; 4944 4945 // Then, evaluate the AddRec. 4946 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 4947 } 4948 4949 return AddRec; 4950 } 4951 4952 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { 4953 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4954 if (Op == Cast->getOperand()) 4955 return Cast; // must be loop invariant 4956 return getZeroExtendExpr(Op, Cast->getType()); 4957 } 4958 4959 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { 4960 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4961 if (Op == Cast->getOperand()) 4962 return Cast; // must be loop invariant 4963 return getSignExtendExpr(Op, Cast->getType()); 4964 } 4965 4966 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { 4967 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4968 if (Op == Cast->getOperand()) 4969 return Cast; // must be loop invariant 4970 return getTruncateExpr(Op, Cast->getType()); 4971 } 4972 4973 llvm_unreachable("Unknown SCEV type!"); 4974 return 0; 4975} 4976 4977/// getSCEVAtScope - This is a convenience function which does 4978/// getSCEVAtScope(getSCEV(V), L). 4979const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 4980 return getSCEVAtScope(getSCEV(V), L); 4981} 4982 4983/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 4984/// following equation: 4985/// 4986/// A * X = B (mod N) 4987/// 4988/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 4989/// A and B isn't important. 4990/// 4991/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 4992static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 4993 ScalarEvolution &SE) { 4994 uint32_t BW = A.getBitWidth(); 4995 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 4996 assert(A != 0 && "A must be non-zero."); 4997 4998 // 1. D = gcd(A, N) 4999 // 5000 // The gcd of A and N may have only one prime factor: 2. The number of 5001 // trailing zeros in A is its multiplicity 5002 uint32_t Mult2 = A.countTrailingZeros(); 5003 // D = 2^Mult2 5004 5005 // 2. Check if B is divisible by D. 5006 // 5007 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 5008 // is not less than multiplicity of this prime factor for D. 5009 if (B.countTrailingZeros() < Mult2) 5010 return SE.getCouldNotCompute(); 5011 5012 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 5013 // modulo (N / D). 5014 // 5015 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 5016 // bit width during computations. 5017 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 5018 APInt Mod(BW + 1, 0); 5019 Mod.setBit(BW - Mult2); // Mod = N / D 5020 APInt I = AD.multiplicativeInverse(Mod); 5021 5022 // 4. Compute the minimum unsigned root of the equation: 5023 // I * (B / D) mod (N / D) 5024 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 5025 5026 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 5027 // bits. 5028 return SE.getConstant(Result.trunc(BW)); 5029} 5030 5031/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 5032/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 5033/// might be the same) or two SCEVCouldNotCompute objects. 5034/// 5035static std::pair<const SCEV *,const SCEV *> 5036SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 5037 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 5038 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 5039 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 5040 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 5041 5042 // We currently can only solve this if the coefficients are constants. 5043 if (!LC || !MC || !NC) { 5044 const SCEV *CNC = SE.getCouldNotCompute(); 5045 return std::make_pair(CNC, CNC); 5046 } 5047 5048 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 5049 const APInt &L = LC->getValue()->getValue(); 5050 const APInt &M = MC->getValue()->getValue(); 5051 const APInt &N = NC->getValue()->getValue(); 5052 APInt Two(BitWidth, 2); 5053 APInt Four(BitWidth, 4); 5054 5055 { 5056 using namespace APIntOps; 5057 const APInt& C = L; 5058 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 5059 // The B coefficient is M-N/2 5060 APInt B(M); 5061 B -= sdiv(N,Two); 5062 5063 // The A coefficient is N/2 5064 APInt A(N.sdiv(Two)); 5065 5066 // Compute the B^2-4ac term. 5067 APInt SqrtTerm(B); 5068 SqrtTerm *= B; 5069 SqrtTerm -= Four * (A * C); 5070 5071 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 5072 // integer value or else APInt::sqrt() will assert. 5073 APInt SqrtVal(SqrtTerm.sqrt()); 5074 5075 // Compute the two solutions for the quadratic formula. 5076 // The divisions must be performed as signed divisions. 5077 APInt NegB(-B); 5078 APInt TwoA( A << 1 ); 5079 if (TwoA.isMinValue()) { 5080 const SCEV *CNC = SE.getCouldNotCompute(); 5081 return std::make_pair(CNC, CNC); 5082 } 5083 5084 LLVMContext &Context = SE.getContext(); 5085 5086 ConstantInt *Solution1 = 5087 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA)); 5088 ConstantInt *Solution2 = 5089 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA)); 5090 5091 return std::make_pair(SE.getConstant(Solution1), 5092 SE.getConstant(Solution2)); 5093 } // end APIntOps namespace 5094} 5095 5096/// HowFarToZero - Return the number of times a backedge comparing the specified 5097/// value to zero will execute. If not computable, return CouldNotCompute. 5098/// 5099/// This is only used for loops with a "x != y" exit test. The exit condition is 5100/// now expressed as a single expression, V = x-y. So the exit test is 5101/// effectively V != 0. We know and take advantage of the fact that this 5102/// expression only being used in a comparison by zero context. 5103ScalarEvolution::ExitLimit 5104ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) { 5105 // If the value is a constant 5106 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 5107 // If the value is already zero, the branch will execute zero times. 5108 if (C->getValue()->isZero()) return C; 5109 return getCouldNotCompute(); // Otherwise it will loop infinitely. 5110 } 5111 5112 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 5113 if (!AddRec || AddRec->getLoop() != L) 5114 return getCouldNotCompute(); 5115 5116 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 5117 // the quadratic equation to solve it. 5118 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) { 5119 std::pair<const SCEV *,const SCEV *> Roots = 5120 SolveQuadraticEquation(AddRec, *this); 5121 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 5122 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 5123 if (R1 && R2) { 5124#if 0 5125 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1 5126 << " sol#2: " << *R2 << "\n"; 5127#endif 5128 // Pick the smallest positive root value. 5129 if (ConstantInt *CB = 5130 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT, 5131 R1->getValue(), 5132 R2->getValue()))) { 5133 if (CB->getZExtValue() == false) 5134 std::swap(R1, R2); // R1 is the minimum root now. 5135 5136 // We can only use this value if the chrec ends up with an exact zero 5137 // value at this index. When solving for "X*X != 5", for example, we 5138 // should not accept a root of 2. 5139 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this); 5140 if (Val->isZero()) 5141 return R1; // We found a quadratic root! 5142 } 5143 } 5144 return getCouldNotCompute(); 5145 } 5146 5147 // Otherwise we can only handle this if it is affine. 5148 if (!AddRec->isAffine()) 5149 return getCouldNotCompute(); 5150 5151 // If this is an affine expression, the execution count of this branch is 5152 // the minimum unsigned root of the following equation: 5153 // 5154 // Start + Step*N = 0 (mod 2^BW) 5155 // 5156 // equivalent to: 5157 // 5158 // Step*N = -Start (mod 2^BW) 5159 // 5160 // where BW is the common bit width of Start and Step. 5161 5162 // Get the initial value for the loop. 5163 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 5164 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop()); 5165 5166 // For now we handle only constant steps. 5167 // 5168 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the 5169 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap 5170 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step. 5171 // We have not yet seen any such cases. 5172 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step); 5173 if (StepC == 0) 5174 return getCouldNotCompute(); 5175 5176 // For positive steps (counting up until unsigned overflow): 5177 // N = -Start/Step (as unsigned) 5178 // For negative steps (counting down to zero): 5179 // N = Start/-Step 5180 // First compute the unsigned distance from zero in the direction of Step. 5181 bool CountDown = StepC->getValue()->getValue().isNegative(); 5182 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start); 5183 5184 // Handle unitary steps, which cannot wraparound. 5185 // 1*N = -Start; -1*N = Start (mod 2^BW), so: 5186 // N = Distance (as unsigned) 5187 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) 5188 return Distance; 5189 5190 // If the recurrence is known not to wraparound, unsigned divide computes the 5191 // back edge count. We know that the value will either become zero (and thus 5192 // the loop terminates), that the loop will terminate through some other exit 5193 // condition first, or that the loop has undefined behavior. This means 5194 // we can't "miss" the exit value, even with nonunit stride. 5195 // 5196 // FIXME: Prove that loops always exhibits *acceptable* undefined 5197 // behavior. Loops must exhibit defined behavior until a wrapped value is 5198 // actually used. So the trip count computed by udiv could be smaller than the 5199 // number of well-defined iterations. 5200 if (AddRec->getNoWrapFlags(SCEV::FlagNW)) 5201 // FIXME: We really want an "isexact" bit for udiv. 5202 return getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step); 5203 5204 // Then, try to solve the above equation provided that Start is constant. 5205 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 5206 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 5207 -StartC->getValue()->getValue(), 5208 *this); 5209 return getCouldNotCompute(); 5210} 5211 5212/// HowFarToNonZero - Return the number of times a backedge checking the 5213/// specified value for nonzero will execute. If not computable, return 5214/// CouldNotCompute 5215ScalarEvolution::ExitLimit 5216ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) { 5217 // Loops that look like: while (X == 0) are very strange indeed. We don't 5218 // handle them yet except for the trivial case. This could be expanded in the 5219 // future as needed. 5220 5221 // If the value is a constant, check to see if it is known to be non-zero 5222 // already. If so, the backedge will execute zero times. 5223 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 5224 if (!C->getValue()->isNullValue()) 5225 return getConstant(C->getType(), 0); 5226 return getCouldNotCompute(); // Otherwise it will loop infinitely. 5227 } 5228 5229 // We could implement others, but I really doubt anyone writes loops like 5230 // this, and if they did, they would already be constant folded. 5231 return getCouldNotCompute(); 5232} 5233 5234/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 5235/// (which may not be an immediate predecessor) which has exactly one 5236/// successor from which BB is reachable, or null if no such block is 5237/// found. 5238/// 5239std::pair<BasicBlock *, BasicBlock *> 5240ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 5241 // If the block has a unique predecessor, then there is no path from the 5242 // predecessor to the block that does not go through the direct edge 5243 // from the predecessor to the block. 5244 if (BasicBlock *Pred = BB->getSinglePredecessor()) 5245 return std::make_pair(Pred, BB); 5246 5247 // A loop's header is defined to be a block that dominates the loop. 5248 // If the header has a unique predecessor outside the loop, it must be 5249 // a block that has exactly one successor that can reach the loop. 5250 if (Loop *L = LI->getLoopFor(BB)) 5251 return std::make_pair(L->getLoopPredecessor(), L->getHeader()); 5252 5253 return std::pair<BasicBlock *, BasicBlock *>(); 5254} 5255 5256/// HasSameValue - SCEV structural equivalence is usually sufficient for 5257/// testing whether two expressions are equal, however for the purposes of 5258/// looking for a condition guarding a loop, it can be useful to be a little 5259/// more general, since a front-end may have replicated the controlling 5260/// expression. 5261/// 5262static bool HasSameValue(const SCEV *A, const SCEV *B) { 5263 // Quick check to see if they are the same SCEV. 5264 if (A == B) return true; 5265 5266 // Otherwise, if they're both SCEVUnknown, it's possible that they hold 5267 // two different instructions with the same value. Check for this case. 5268 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A)) 5269 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B)) 5270 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue())) 5271 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue())) 5272 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory()) 5273 return true; 5274 5275 // Otherwise assume they may have a different value. 5276 return false; 5277} 5278 5279/// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with 5280/// predicate Pred. Return true iff any changes were made. 5281/// 5282bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred, 5283 const SCEV *&LHS, const SCEV *&RHS) { 5284 bool Changed = false; 5285 5286 // Canonicalize a constant to the right side. 5287 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 5288 // Check for both operands constant. 5289 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 5290 if (ConstantExpr::getICmp(Pred, 5291 LHSC->getValue(), 5292 RHSC->getValue())->isNullValue()) 5293 goto trivially_false; 5294 else 5295 goto trivially_true; 5296 } 5297 // Otherwise swap the operands to put the constant on the right. 5298 std::swap(LHS, RHS); 5299 Pred = ICmpInst::getSwappedPredicate(Pred); 5300 Changed = true; 5301 } 5302 5303 // If we're comparing an addrec with a value which is loop-invariant in the 5304 // addrec's loop, put the addrec on the left. Also make a dominance check, 5305 // as both operands could be addrecs loop-invariant in each other's loop. 5306 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) { 5307 const Loop *L = AR->getLoop(); 5308 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) { 5309 std::swap(LHS, RHS); 5310 Pred = ICmpInst::getSwappedPredicate(Pred); 5311 Changed = true; 5312 } 5313 } 5314 5315 // If there's a constant operand, canonicalize comparisons with boundary 5316 // cases, and canonicalize *-or-equal comparisons to regular comparisons. 5317 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) { 5318 const APInt &RA = RC->getValue()->getValue(); 5319 switch (Pred) { 5320 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5321 case ICmpInst::ICMP_EQ: 5322 case ICmpInst::ICMP_NE: 5323 break; 5324 case ICmpInst::ICMP_UGE: 5325 if ((RA - 1).isMinValue()) { 5326 Pred = ICmpInst::ICMP_NE; 5327 RHS = getConstant(RA - 1); 5328 Changed = true; 5329 break; 5330 } 5331 if (RA.isMaxValue()) { 5332 Pred = ICmpInst::ICMP_EQ; 5333 Changed = true; 5334 break; 5335 } 5336 if (RA.isMinValue()) goto trivially_true; 5337 5338 Pred = ICmpInst::ICMP_UGT; 5339 RHS = getConstant(RA - 1); 5340 Changed = true; 5341 break; 5342 case ICmpInst::ICMP_ULE: 5343 if ((RA + 1).isMaxValue()) { 5344 Pred = ICmpInst::ICMP_NE; 5345 RHS = getConstant(RA + 1); 5346 Changed = true; 5347 break; 5348 } 5349 if (RA.isMinValue()) { 5350 Pred = ICmpInst::ICMP_EQ; 5351 Changed = true; 5352 break; 5353 } 5354 if (RA.isMaxValue()) goto trivially_true; 5355 5356 Pred = ICmpInst::ICMP_ULT; 5357 RHS = getConstant(RA + 1); 5358 Changed = true; 5359 break; 5360 case ICmpInst::ICMP_SGE: 5361 if ((RA - 1).isMinSignedValue()) { 5362 Pred = ICmpInst::ICMP_NE; 5363 RHS = getConstant(RA - 1); 5364 Changed = true; 5365 break; 5366 } 5367 if (RA.isMaxSignedValue()) { 5368 Pred = ICmpInst::ICMP_EQ; 5369 Changed = true; 5370 break; 5371 } 5372 if (RA.isMinSignedValue()) goto trivially_true; 5373 5374 Pred = ICmpInst::ICMP_SGT; 5375 RHS = getConstant(RA - 1); 5376 Changed = true; 5377 break; 5378 case ICmpInst::ICMP_SLE: 5379 if ((RA + 1).isMaxSignedValue()) { 5380 Pred = ICmpInst::ICMP_NE; 5381 RHS = getConstant(RA + 1); 5382 Changed = true; 5383 break; 5384 } 5385 if (RA.isMinSignedValue()) { 5386 Pred = ICmpInst::ICMP_EQ; 5387 Changed = true; 5388 break; 5389 } 5390 if (RA.isMaxSignedValue()) goto trivially_true; 5391 5392 Pred = ICmpInst::ICMP_SLT; 5393 RHS = getConstant(RA + 1); 5394 Changed = true; 5395 break; 5396 case ICmpInst::ICMP_UGT: 5397 if (RA.isMinValue()) { 5398 Pred = ICmpInst::ICMP_NE; 5399 Changed = true; 5400 break; 5401 } 5402 if ((RA + 1).isMaxValue()) { 5403 Pred = ICmpInst::ICMP_EQ; 5404 RHS = getConstant(RA + 1); 5405 Changed = true; 5406 break; 5407 } 5408 if (RA.isMaxValue()) goto trivially_false; 5409 break; 5410 case ICmpInst::ICMP_ULT: 5411 if (RA.isMaxValue()) { 5412 Pred = ICmpInst::ICMP_NE; 5413 Changed = true; 5414 break; 5415 } 5416 if ((RA - 1).isMinValue()) { 5417 Pred = ICmpInst::ICMP_EQ; 5418 RHS = getConstant(RA - 1); 5419 Changed = true; 5420 break; 5421 } 5422 if (RA.isMinValue()) goto trivially_false; 5423 break; 5424 case ICmpInst::ICMP_SGT: 5425 if (RA.isMinSignedValue()) { 5426 Pred = ICmpInst::ICMP_NE; 5427 Changed = true; 5428 break; 5429 } 5430 if ((RA + 1).isMaxSignedValue()) { 5431 Pred = ICmpInst::ICMP_EQ; 5432 RHS = getConstant(RA + 1); 5433 Changed = true; 5434 break; 5435 } 5436 if (RA.isMaxSignedValue()) goto trivially_false; 5437 break; 5438 case ICmpInst::ICMP_SLT: 5439 if (RA.isMaxSignedValue()) { 5440 Pred = ICmpInst::ICMP_NE; 5441 Changed = true; 5442 break; 5443 } 5444 if ((RA - 1).isMinSignedValue()) { 5445 Pred = ICmpInst::ICMP_EQ; 5446 RHS = getConstant(RA - 1); 5447 Changed = true; 5448 break; 5449 } 5450 if (RA.isMinSignedValue()) goto trivially_false; 5451 break; 5452 } 5453 } 5454 5455 // Check for obvious equality. 5456 if (HasSameValue(LHS, RHS)) { 5457 if (ICmpInst::isTrueWhenEqual(Pred)) 5458 goto trivially_true; 5459 if (ICmpInst::isFalseWhenEqual(Pred)) 5460 goto trivially_false; 5461 } 5462 5463 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by 5464 // adding or subtracting 1 from one of the operands. 5465 switch (Pred) { 5466 case ICmpInst::ICMP_SLE: 5467 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) { 5468 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 5469 SCEV::FlagNSW); 5470 Pred = ICmpInst::ICMP_SLT; 5471 Changed = true; 5472 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) { 5473 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 5474 SCEV::FlagNSW); 5475 Pred = ICmpInst::ICMP_SLT; 5476 Changed = true; 5477 } 5478 break; 5479 case ICmpInst::ICMP_SGE: 5480 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) { 5481 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 5482 SCEV::FlagNSW); 5483 Pred = ICmpInst::ICMP_SGT; 5484 Changed = true; 5485 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) { 5486 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 5487 SCEV::FlagNSW); 5488 Pred = ICmpInst::ICMP_SGT; 5489 Changed = true; 5490 } 5491 break; 5492 case ICmpInst::ICMP_ULE: 5493 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) { 5494 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 5495 SCEV::FlagNUW); 5496 Pred = ICmpInst::ICMP_ULT; 5497 Changed = true; 5498 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) { 5499 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 5500 SCEV::FlagNUW); 5501 Pred = ICmpInst::ICMP_ULT; 5502 Changed = true; 5503 } 5504 break; 5505 case ICmpInst::ICMP_UGE: 5506 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) { 5507 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 5508 SCEV::FlagNUW); 5509 Pred = ICmpInst::ICMP_UGT; 5510 Changed = true; 5511 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) { 5512 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 5513 SCEV::FlagNUW); 5514 Pred = ICmpInst::ICMP_UGT; 5515 Changed = true; 5516 } 5517 break; 5518 default: 5519 break; 5520 } 5521 5522 // TODO: More simplifications are possible here. 5523 5524 return Changed; 5525 5526trivially_true: 5527 // Return 0 == 0. 5528 LHS = RHS = getConstant(ConstantInt::getFalse(getContext())); 5529 Pred = ICmpInst::ICMP_EQ; 5530 return true; 5531 5532trivially_false: 5533 // Return 0 != 0. 5534 LHS = RHS = getConstant(ConstantInt::getFalse(getContext())); 5535 Pred = ICmpInst::ICMP_NE; 5536 return true; 5537} 5538 5539bool ScalarEvolution::isKnownNegative(const SCEV *S) { 5540 return getSignedRange(S).getSignedMax().isNegative(); 5541} 5542 5543bool ScalarEvolution::isKnownPositive(const SCEV *S) { 5544 return getSignedRange(S).getSignedMin().isStrictlyPositive(); 5545} 5546 5547bool ScalarEvolution::isKnownNonNegative(const SCEV *S) { 5548 return !getSignedRange(S).getSignedMin().isNegative(); 5549} 5550 5551bool ScalarEvolution::isKnownNonPositive(const SCEV *S) { 5552 return !getSignedRange(S).getSignedMax().isStrictlyPositive(); 5553} 5554 5555bool ScalarEvolution::isKnownNonZero(const SCEV *S) { 5556 return isKnownNegative(S) || isKnownPositive(S); 5557} 5558 5559bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred, 5560 const SCEV *LHS, const SCEV *RHS) { 5561 // Canonicalize the inputs first. 5562 (void)SimplifyICmpOperands(Pred, LHS, RHS); 5563 5564 // If LHS or RHS is an addrec, check to see if the condition is true in 5565 // every iteration of the loop. 5566 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 5567 if (isLoopEntryGuardedByCond( 5568 AR->getLoop(), Pred, AR->getStart(), RHS) && 5569 isLoopBackedgeGuardedByCond( 5570 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS)) 5571 return true; 5572 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) 5573 if (isLoopEntryGuardedByCond( 5574 AR->getLoop(), Pred, LHS, AR->getStart()) && 5575 isLoopBackedgeGuardedByCond( 5576 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this))) 5577 return true; 5578 5579 // Otherwise see what can be done with known constant ranges. 5580 return isKnownPredicateWithRanges(Pred, LHS, RHS); 5581} 5582 5583bool 5584ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred, 5585 const SCEV *LHS, const SCEV *RHS) { 5586 if (HasSameValue(LHS, RHS)) 5587 return ICmpInst::isTrueWhenEqual(Pred); 5588 5589 // This code is split out from isKnownPredicate because it is called from 5590 // within isLoopEntryGuardedByCond. 5591 switch (Pred) { 5592 default: 5593 llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5594 break; 5595 case ICmpInst::ICMP_SGT: 5596 Pred = ICmpInst::ICMP_SLT; 5597 std::swap(LHS, RHS); 5598 case ICmpInst::ICMP_SLT: { 5599 ConstantRange LHSRange = getSignedRange(LHS); 5600 ConstantRange RHSRange = getSignedRange(RHS); 5601 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin())) 5602 return true; 5603 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax())) 5604 return false; 5605 break; 5606 } 5607 case ICmpInst::ICMP_SGE: 5608 Pred = ICmpInst::ICMP_SLE; 5609 std::swap(LHS, RHS); 5610 case ICmpInst::ICMP_SLE: { 5611 ConstantRange LHSRange = getSignedRange(LHS); 5612 ConstantRange RHSRange = getSignedRange(RHS); 5613 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin())) 5614 return true; 5615 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax())) 5616 return false; 5617 break; 5618 } 5619 case ICmpInst::ICMP_UGT: 5620 Pred = ICmpInst::ICMP_ULT; 5621 std::swap(LHS, RHS); 5622 case ICmpInst::ICMP_ULT: { 5623 ConstantRange LHSRange = getUnsignedRange(LHS); 5624 ConstantRange RHSRange = getUnsignedRange(RHS); 5625 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin())) 5626 return true; 5627 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax())) 5628 return false; 5629 break; 5630 } 5631 case ICmpInst::ICMP_UGE: 5632 Pred = ICmpInst::ICMP_ULE; 5633 std::swap(LHS, RHS); 5634 case ICmpInst::ICMP_ULE: { 5635 ConstantRange LHSRange = getUnsignedRange(LHS); 5636 ConstantRange RHSRange = getUnsignedRange(RHS); 5637 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin())) 5638 return true; 5639 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax())) 5640 return false; 5641 break; 5642 } 5643 case ICmpInst::ICMP_NE: { 5644 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet()) 5645 return true; 5646 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet()) 5647 return true; 5648 5649 const SCEV *Diff = getMinusSCEV(LHS, RHS); 5650 if (isKnownNonZero(Diff)) 5651 return true; 5652 break; 5653 } 5654 case ICmpInst::ICMP_EQ: 5655 // The check at the top of the function catches the case where 5656 // the values are known to be equal. 5657 break; 5658 } 5659 return false; 5660} 5661 5662/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is 5663/// protected by a conditional between LHS and RHS. This is used to 5664/// to eliminate casts. 5665bool 5666ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L, 5667 ICmpInst::Predicate Pred, 5668 const SCEV *LHS, const SCEV *RHS) { 5669 // Interpret a null as meaning no loop, where there is obviously no guard 5670 // (interprocedural conditions notwithstanding). 5671 if (!L) return true; 5672 5673 BasicBlock *Latch = L->getLoopLatch(); 5674 if (!Latch) 5675 return false; 5676 5677 BranchInst *LoopContinuePredicate = 5678 dyn_cast<BranchInst>(Latch->getTerminator()); 5679 if (!LoopContinuePredicate || 5680 LoopContinuePredicate->isUnconditional()) 5681 return false; 5682 5683 return isImpliedCond(Pred, LHS, RHS, 5684 LoopContinuePredicate->getCondition(), 5685 LoopContinuePredicate->getSuccessor(0) != L->getHeader()); 5686} 5687 5688/// isLoopEntryGuardedByCond - Test whether entry to the loop is protected 5689/// by a conditional between LHS and RHS. This is used to help avoid max 5690/// expressions in loop trip counts, and to eliminate casts. 5691bool 5692ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L, 5693 ICmpInst::Predicate Pred, 5694 const SCEV *LHS, const SCEV *RHS) { 5695 // Interpret a null as meaning no loop, where there is obviously no guard 5696 // (interprocedural conditions notwithstanding). 5697 if (!L) return false; 5698 5699 // Starting at the loop predecessor, climb up the predecessor chain, as long 5700 // as there are predecessors that can be found that have unique successors 5701 // leading to the original header. 5702 for (std::pair<BasicBlock *, BasicBlock *> 5703 Pair(L->getLoopPredecessor(), L->getHeader()); 5704 Pair.first; 5705 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) { 5706 5707 BranchInst *LoopEntryPredicate = 5708 dyn_cast<BranchInst>(Pair.first->getTerminator()); 5709 if (!LoopEntryPredicate || 5710 LoopEntryPredicate->isUnconditional()) 5711 continue; 5712 5713 if (isImpliedCond(Pred, LHS, RHS, 5714 LoopEntryPredicate->getCondition(), 5715 LoopEntryPredicate->getSuccessor(0) != Pair.second)) 5716 return true; 5717 } 5718 5719 return false; 5720} 5721 5722/// isImpliedCond - Test whether the condition described by Pred, LHS, 5723/// and RHS is true whenever the given Cond value evaluates to true. 5724bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, 5725 const SCEV *LHS, const SCEV *RHS, 5726 Value *FoundCondValue, 5727 bool Inverse) { 5728 // Recursively handle And and Or conditions. 5729 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) { 5730 if (BO->getOpcode() == Instruction::And) { 5731 if (!Inverse) 5732 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || 5733 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); 5734 } else if (BO->getOpcode() == Instruction::Or) { 5735 if (Inverse) 5736 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || 5737 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); 5738 } 5739 } 5740 5741 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue); 5742 if (!ICI) return false; 5743 5744 // Bail if the ICmp's operands' types are wider than the needed type 5745 // before attempting to call getSCEV on them. This avoids infinite 5746 // recursion, since the analysis of widening casts can require loop 5747 // exit condition information for overflow checking, which would 5748 // lead back here. 5749 if (getTypeSizeInBits(LHS->getType()) < 5750 getTypeSizeInBits(ICI->getOperand(0)->getType())) 5751 return false; 5752 5753 // Now that we found a conditional branch that dominates the loop, check to 5754 // see if it is the comparison we are looking for. 5755 ICmpInst::Predicate FoundPred; 5756 if (Inverse) 5757 FoundPred = ICI->getInversePredicate(); 5758 else 5759 FoundPred = ICI->getPredicate(); 5760 5761 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0)); 5762 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1)); 5763 5764 // Balance the types. The case where FoundLHS' type is wider than 5765 // LHS' type is checked for above. 5766 if (getTypeSizeInBits(LHS->getType()) > 5767 getTypeSizeInBits(FoundLHS->getType())) { 5768 if (CmpInst::isSigned(Pred)) { 5769 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType()); 5770 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType()); 5771 } else { 5772 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType()); 5773 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType()); 5774 } 5775 } 5776 5777 // Canonicalize the query to match the way instcombine will have 5778 // canonicalized the comparison. 5779 if (SimplifyICmpOperands(Pred, LHS, RHS)) 5780 if (LHS == RHS) 5781 return CmpInst::isTrueWhenEqual(Pred); 5782 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS)) 5783 if (FoundLHS == FoundRHS) 5784 return CmpInst::isFalseWhenEqual(Pred); 5785 5786 // Check to see if we can make the LHS or RHS match. 5787 if (LHS == FoundRHS || RHS == FoundLHS) { 5788 if (isa<SCEVConstant>(RHS)) { 5789 std::swap(FoundLHS, FoundRHS); 5790 FoundPred = ICmpInst::getSwappedPredicate(FoundPred); 5791 } else { 5792 std::swap(LHS, RHS); 5793 Pred = ICmpInst::getSwappedPredicate(Pred); 5794 } 5795 } 5796 5797 // Check whether the found predicate is the same as the desired predicate. 5798 if (FoundPred == Pred) 5799 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS); 5800 5801 // Check whether swapping the found predicate makes it the same as the 5802 // desired predicate. 5803 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) { 5804 if (isa<SCEVConstant>(RHS)) 5805 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS); 5806 else 5807 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred), 5808 RHS, LHS, FoundLHS, FoundRHS); 5809 } 5810 5811 // Check whether the actual condition is beyond sufficient. 5812 if (FoundPred == ICmpInst::ICMP_EQ) 5813 if (ICmpInst::isTrueWhenEqual(Pred)) 5814 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS)) 5815 return true; 5816 if (Pred == ICmpInst::ICMP_NE) 5817 if (!ICmpInst::isTrueWhenEqual(FoundPred)) 5818 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS)) 5819 return true; 5820 5821 // Otherwise assume the worst. 5822 return false; 5823} 5824 5825/// isImpliedCondOperands - Test whether the condition described by Pred, 5826/// LHS, and RHS is true whenever the condition described by Pred, FoundLHS, 5827/// and FoundRHS is true. 5828bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred, 5829 const SCEV *LHS, const SCEV *RHS, 5830 const SCEV *FoundLHS, 5831 const SCEV *FoundRHS) { 5832 return isImpliedCondOperandsHelper(Pred, LHS, RHS, 5833 FoundLHS, FoundRHS) || 5834 // ~x < ~y --> x > y 5835 isImpliedCondOperandsHelper(Pred, LHS, RHS, 5836 getNotSCEV(FoundRHS), 5837 getNotSCEV(FoundLHS)); 5838} 5839 5840/// isImpliedCondOperandsHelper - Test whether the condition described by 5841/// Pred, LHS, and RHS is true whenever the condition described by Pred, 5842/// FoundLHS, and FoundRHS is true. 5843bool 5844ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred, 5845 const SCEV *LHS, const SCEV *RHS, 5846 const SCEV *FoundLHS, 5847 const SCEV *FoundRHS) { 5848 switch (Pred) { 5849 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5850 case ICmpInst::ICMP_EQ: 5851 case ICmpInst::ICMP_NE: 5852 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS)) 5853 return true; 5854 break; 5855 case ICmpInst::ICMP_SLT: 5856 case ICmpInst::ICMP_SLE: 5857 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) && 5858 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS)) 5859 return true; 5860 break; 5861 case ICmpInst::ICMP_SGT: 5862 case ICmpInst::ICMP_SGE: 5863 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) && 5864 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS)) 5865 return true; 5866 break; 5867 case ICmpInst::ICMP_ULT: 5868 case ICmpInst::ICMP_ULE: 5869 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) && 5870 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS)) 5871 return true; 5872 break; 5873 case ICmpInst::ICMP_UGT: 5874 case ICmpInst::ICMP_UGE: 5875 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) && 5876 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS)) 5877 return true; 5878 break; 5879 } 5880 5881 return false; 5882} 5883 5884/// getBECount - Subtract the end and start values and divide by the step, 5885/// rounding up, to get the number of times the backedge is executed. Return 5886/// CouldNotCompute if an intermediate computation overflows. 5887const SCEV *ScalarEvolution::getBECount(const SCEV *Start, 5888 const SCEV *End, 5889 const SCEV *Step, 5890 bool NoWrap) { 5891 assert(!isKnownNegative(Step) && 5892 "This code doesn't handle negative strides yet!"); 5893 5894 Type *Ty = Start->getType(); 5895 5896 // When Start == End, we have an exact BECount == 0. Short-circuit this case 5897 // here because SCEV may not be able to determine that the unsigned division 5898 // after rounding is zero. 5899 if (Start == End) 5900 return getConstant(Ty, 0); 5901 5902 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1); 5903 const SCEV *Diff = getMinusSCEV(End, Start); 5904 const SCEV *RoundUp = getAddExpr(Step, NegOne); 5905 5906 // Add an adjustment to the difference between End and Start so that 5907 // the division will effectively round up. 5908 const SCEV *Add = getAddExpr(Diff, RoundUp); 5909 5910 if (!NoWrap) { 5911 // Check Add for unsigned overflow. 5912 // TODO: More sophisticated things could be done here. 5913 Type *WideTy = IntegerType::get(getContext(), 5914 getTypeSizeInBits(Ty) + 1); 5915 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy); 5916 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy); 5917 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp); 5918 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd) 5919 return getCouldNotCompute(); 5920 } 5921 5922 return getUDivExpr(Add, Step); 5923} 5924 5925/// HowManyLessThans - Return the number of times a backedge containing the 5926/// specified less-than comparison will execute. If not computable, return 5927/// CouldNotCompute. 5928ScalarEvolution::ExitLimit 5929ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS, 5930 const Loop *L, bool isSigned) { 5931 // Only handle: "ADDREC < LoopInvariant". 5932 if (!isLoopInvariant(RHS, L)) return getCouldNotCompute(); 5933 5934 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 5935 if (!AddRec || AddRec->getLoop() != L) 5936 return getCouldNotCompute(); 5937 5938 // Check to see if we have a flag which makes analysis easy. 5939 bool NoWrap = isSigned ? AddRec->getNoWrapFlags(SCEV::FlagNSW) : 5940 AddRec->getNoWrapFlags(SCEV::FlagNUW); 5941 5942 if (AddRec->isAffine()) { 5943 unsigned BitWidth = getTypeSizeInBits(AddRec->getType()); 5944 const SCEV *Step = AddRec->getStepRecurrence(*this); 5945 5946 if (Step->isZero()) 5947 return getCouldNotCompute(); 5948 if (Step->isOne()) { 5949 // With unit stride, the iteration never steps past the limit value. 5950 } else if (isKnownPositive(Step)) { 5951 // Test whether a positive iteration can step past the limit 5952 // value and past the maximum value for its type in a single step. 5953 // Note that it's not sufficient to check NoWrap here, because even 5954 // though the value after a wrap is undefined, it's not undefined 5955 // behavior, so if wrap does occur, the loop could either terminate or 5956 // loop infinitely, but in either case, the loop is guaranteed to 5957 // iterate at least until the iteration where the wrapping occurs. 5958 const SCEV *One = getConstant(Step->getType(), 1); 5959 if (isSigned) { 5960 APInt Max = APInt::getSignedMaxValue(BitWidth); 5961 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax()) 5962 .slt(getSignedRange(RHS).getSignedMax())) 5963 return getCouldNotCompute(); 5964 } else { 5965 APInt Max = APInt::getMaxValue(BitWidth); 5966 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax()) 5967 .ult(getUnsignedRange(RHS).getUnsignedMax())) 5968 return getCouldNotCompute(); 5969 } 5970 } else 5971 // TODO: Handle negative strides here and below. 5972 return getCouldNotCompute(); 5973 5974 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant 5975 // m. So, we count the number of iterations in which {n,+,s} < m is true. 5976 // Note that we cannot simply return max(m-n,0)/s because it's not safe to 5977 // treat m-n as signed nor unsigned due to overflow possibility. 5978 5979 // First, we get the value of the LHS in the first iteration: n 5980 const SCEV *Start = AddRec->getOperand(0); 5981 5982 // Determine the minimum constant start value. 5983 const SCEV *MinStart = getConstant(isSigned ? 5984 getSignedRange(Start).getSignedMin() : 5985 getUnsignedRange(Start).getUnsignedMin()); 5986 5987 // If we know that the condition is true in order to enter the loop, 5988 // then we know that it will run exactly (m-n)/s times. Otherwise, we 5989 // only know that it will execute (max(m,n)-n)/s times. In both cases, 5990 // the division must round up. 5991 const SCEV *End = RHS; 5992 if (!isLoopEntryGuardedByCond(L, 5993 isSigned ? ICmpInst::ICMP_SLT : 5994 ICmpInst::ICMP_ULT, 5995 getMinusSCEV(Start, Step), RHS)) 5996 End = isSigned ? getSMaxExpr(RHS, Start) 5997 : getUMaxExpr(RHS, Start); 5998 5999 // Determine the maximum constant end value. 6000 const SCEV *MaxEnd = getConstant(isSigned ? 6001 getSignedRange(End).getSignedMax() : 6002 getUnsignedRange(End).getUnsignedMax()); 6003 6004 // If MaxEnd is within a step of the maximum integer value in its type, 6005 // adjust it down to the minimum value which would produce the same effect. 6006 // This allows the subsequent ceiling division of (N+(step-1))/step to 6007 // compute the correct value. 6008 const SCEV *StepMinusOne = getMinusSCEV(Step, 6009 getConstant(Step->getType(), 1)); 6010 MaxEnd = isSigned ? 6011 getSMinExpr(MaxEnd, 6012 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)), 6013 StepMinusOne)) : 6014 getUMinExpr(MaxEnd, 6015 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)), 6016 StepMinusOne)); 6017 6018 // Finally, we subtract these two values and divide, rounding up, to get 6019 // the number of times the backedge is executed. 6020 const SCEV *BECount = getBECount(Start, End, Step, NoWrap); 6021 6022 // The maximum backedge count is similar, except using the minimum start 6023 // value and the maximum end value. 6024 // If we already have an exact constant BECount, use it instead. 6025 const SCEV *MaxBECount = isa<SCEVConstant>(BECount) ? BECount 6026 : getBECount(MinStart, MaxEnd, Step, NoWrap); 6027 6028 // If the stride is nonconstant, and NoWrap == true, then 6029 // getBECount(MinStart, MaxEnd) may not compute. This would result in an 6030 // exact BECount and invalid MaxBECount, which should be avoided to catch 6031 // more optimization opportunities. 6032 if (isa<SCEVCouldNotCompute>(MaxBECount)) 6033 MaxBECount = BECount; 6034 6035 return ExitLimit(BECount, MaxBECount); 6036 } 6037 6038 return getCouldNotCompute(); 6039} 6040 6041/// getNumIterationsInRange - Return the number of iterations of this loop that 6042/// produce values in the specified constant range. Another way of looking at 6043/// this is that it returns the first iteration number where the value is not in 6044/// the condition, thus computing the exit count. If the iteration count can't 6045/// be computed, an instance of SCEVCouldNotCompute is returned. 6046const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 6047 ScalarEvolution &SE) const { 6048 if (Range.isFullSet()) // Infinite loop. 6049 return SE.getCouldNotCompute(); 6050 6051 // If the start is a non-zero constant, shift the range to simplify things. 6052 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 6053 if (!SC->getValue()->isZero()) { 6054 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end()); 6055 Operands[0] = SE.getConstant(SC->getType(), 0); 6056 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(), 6057 getNoWrapFlags(FlagNW)); 6058 if (const SCEVAddRecExpr *ShiftedAddRec = 6059 dyn_cast<SCEVAddRecExpr>(Shifted)) 6060 return ShiftedAddRec->getNumIterationsInRange( 6061 Range.subtract(SC->getValue()->getValue()), SE); 6062 // This is strange and shouldn't happen. 6063 return SE.getCouldNotCompute(); 6064 } 6065 6066 // The only time we can solve this is when we have all constant indices. 6067 // Otherwise, we cannot determine the overflow conditions. 6068 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 6069 if (!isa<SCEVConstant>(getOperand(i))) 6070 return SE.getCouldNotCompute(); 6071 6072 6073 // Okay at this point we know that all elements of the chrec are constants and 6074 // that the start element is zero. 6075 6076 // First check to see if the range contains zero. If not, the first 6077 // iteration exits. 6078 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 6079 if (!Range.contains(APInt(BitWidth, 0))) 6080 return SE.getConstant(getType(), 0); 6081 6082 if (isAffine()) { 6083 // If this is an affine expression then we have this situation: 6084 // Solve {0,+,A} in Range === Ax in Range 6085 6086 // We know that zero is in the range. If A is positive then we know that 6087 // the upper value of the range must be the first possible exit value. 6088 // If A is negative then the lower of the range is the last possible loop 6089 // value. Also note that we already checked for a full range. 6090 APInt One(BitWidth,1); 6091 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 6092 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 6093 6094 // The exit value should be (End+A)/A. 6095 APInt ExitVal = (End + A).udiv(A); 6096 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal); 6097 6098 // Evaluate at the exit value. If we really did fall out of the valid 6099 // range, then we computed our trip count, otherwise wrap around or other 6100 // things must have happened. 6101 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 6102 if (Range.contains(Val->getValue())) 6103 return SE.getCouldNotCompute(); // Something strange happened 6104 6105 // Ensure that the previous value is in the range. This is a sanity check. 6106 assert(Range.contains( 6107 EvaluateConstantChrecAtConstant(this, 6108 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) && 6109 "Linear scev computation is off in a bad way!"); 6110 return SE.getConstant(ExitValue); 6111 } else if (isQuadratic()) { 6112 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 6113 // quadratic equation to solve it. To do this, we must frame our problem in 6114 // terms of figuring out when zero is crossed, instead of when 6115 // Range.getUpper() is crossed. 6116 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end()); 6117 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 6118 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(), 6119 // getNoWrapFlags(FlagNW) 6120 FlagAnyWrap); 6121 6122 // Next, solve the constructed addrec 6123 std::pair<const SCEV *,const SCEV *> Roots = 6124 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 6125 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 6126 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 6127 if (R1) { 6128 // Pick the smallest positive root value. 6129 if (ConstantInt *CB = 6130 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 6131 R1->getValue(), R2->getValue()))) { 6132 if (CB->getZExtValue() == false) 6133 std::swap(R1, R2); // R1 is the minimum root now. 6134 6135 // Make sure the root is not off by one. The returned iteration should 6136 // not be in the range, but the previous one should be. When solving 6137 // for "X*X < 5", for example, we should not return a root of 2. 6138 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 6139 R1->getValue(), 6140 SE); 6141 if (Range.contains(R1Val->getValue())) { 6142 // The next iteration must be out of the range... 6143 ConstantInt *NextVal = 6144 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1); 6145 6146 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 6147 if (!Range.contains(R1Val->getValue())) 6148 return SE.getConstant(NextVal); 6149 return SE.getCouldNotCompute(); // Something strange happened 6150 } 6151 6152 // If R1 was not in the range, then it is a good return value. Make 6153 // sure that R1-1 WAS in the range though, just in case. 6154 ConstantInt *NextVal = 6155 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1); 6156 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 6157 if (Range.contains(R1Val->getValue())) 6158 return R1; 6159 return SE.getCouldNotCompute(); // Something strange happened 6160 } 6161 } 6162 } 6163 6164 return SE.getCouldNotCompute(); 6165} 6166 6167 6168 6169//===----------------------------------------------------------------------===// 6170// SCEVCallbackVH Class Implementation 6171//===----------------------------------------------------------------------===// 6172 6173void ScalarEvolution::SCEVCallbackVH::deleted() { 6174 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 6175 if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) 6176 SE->ConstantEvolutionLoopExitValue.erase(PN); 6177 SE->ValueExprMap.erase(getValPtr()); 6178 // this now dangles! 6179} 6180 6181void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) { 6182 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 6183 6184 // Forget all the expressions associated with users of the old value, 6185 // so that future queries will recompute the expressions using the new 6186 // value. 6187 Value *Old = getValPtr(); 6188 SmallVector<User *, 16> Worklist; 6189 SmallPtrSet<User *, 8> Visited; 6190 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end(); 6191 UI != UE; ++UI) 6192 Worklist.push_back(*UI); 6193 while (!Worklist.empty()) { 6194 User *U = Worklist.pop_back_val(); 6195 // Deleting the Old value will cause this to dangle. Postpone 6196 // that until everything else is done. 6197 if (U == Old) 6198 continue; 6199 if (!Visited.insert(U)) 6200 continue; 6201 if (PHINode *PN = dyn_cast<PHINode>(U)) 6202 SE->ConstantEvolutionLoopExitValue.erase(PN); 6203 SE->ValueExprMap.erase(U); 6204 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end(); 6205 UI != UE; ++UI) 6206 Worklist.push_back(*UI); 6207 } 6208 // Delete the Old value. 6209 if (PHINode *PN = dyn_cast<PHINode>(Old)) 6210 SE->ConstantEvolutionLoopExitValue.erase(PN); 6211 SE->ValueExprMap.erase(Old); 6212 // this now dangles! 6213} 6214 6215ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) 6216 : CallbackVH(V), SE(se) {} 6217 6218//===----------------------------------------------------------------------===// 6219// ScalarEvolution Class Implementation 6220//===----------------------------------------------------------------------===// 6221 6222ScalarEvolution::ScalarEvolution() 6223 : FunctionPass(ID), FirstUnknown(0) { 6224 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry()); 6225} 6226 6227bool ScalarEvolution::runOnFunction(Function &F) { 6228 this->F = &F; 6229 LI = &getAnalysis<LoopInfo>(); 6230 TD = getAnalysisIfAvailable<TargetData>(); 6231 DT = &getAnalysis<DominatorTree>(); 6232 return false; 6233} 6234 6235void ScalarEvolution::releaseMemory() { 6236 // Iterate through all the SCEVUnknown instances and call their 6237 // destructors, so that they release their references to their values. 6238 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next) 6239 U->~SCEVUnknown(); 6240 FirstUnknown = 0; 6241 6242 ValueExprMap.clear(); 6243 6244 // Free any extra memory created for ExitNotTakenInfo in the unlikely event 6245 // that a loop had multiple computable exits. 6246 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I = 6247 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); 6248 I != E; ++I) { 6249 I->second.clear(); 6250 } 6251 6252 BackedgeTakenCounts.clear(); 6253 ConstantEvolutionLoopExitValue.clear(); 6254 ValuesAtScopes.clear(); 6255 LoopDispositions.clear(); 6256 BlockDispositions.clear(); 6257 UnsignedRanges.clear(); 6258 SignedRanges.clear(); 6259 UniqueSCEVs.clear(); 6260 SCEVAllocator.Reset(); 6261} 6262 6263void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 6264 AU.setPreservesAll(); 6265 AU.addRequiredTransitive<LoopInfo>(); 6266 AU.addRequiredTransitive<DominatorTree>(); 6267} 6268 6269bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 6270 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 6271} 6272 6273static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 6274 const Loop *L) { 6275 // Print all inner loops first 6276 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 6277 PrintLoopInfo(OS, SE, *I); 6278 6279 OS << "Loop "; 6280 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 6281 OS << ": "; 6282 6283 SmallVector<BasicBlock *, 8> ExitBlocks; 6284 L->getExitBlocks(ExitBlocks); 6285 if (ExitBlocks.size() != 1) 6286 OS << "<multiple exits> "; 6287 6288 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 6289 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 6290 } else { 6291 OS << "Unpredictable backedge-taken count. "; 6292 } 6293 6294 OS << "\n" 6295 "Loop "; 6296 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 6297 OS << ": "; 6298 6299 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) { 6300 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L); 6301 } else { 6302 OS << "Unpredictable max backedge-taken count. "; 6303 } 6304 6305 OS << "\n"; 6306} 6307 6308void ScalarEvolution::print(raw_ostream &OS, const Module *) const { 6309 // ScalarEvolution's implementation of the print method is to print 6310 // out SCEV values of all instructions that are interesting. Doing 6311 // this potentially causes it to create new SCEV objects though, 6312 // which technically conflicts with the const qualifier. This isn't 6313 // observable from outside the class though, so casting away the 6314 // const isn't dangerous. 6315 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this); 6316 6317 OS << "Classifying expressions for: "; 6318 WriteAsOperand(OS, F, /*PrintType=*/false); 6319 OS << "\n"; 6320 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 6321 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) { 6322 OS << *I << '\n'; 6323 OS << " --> "; 6324 const SCEV *SV = SE.getSCEV(&*I); 6325 SV->print(OS); 6326 6327 const Loop *L = LI->getLoopFor((*I).getParent()); 6328 6329 const SCEV *AtUse = SE.getSCEVAtScope(SV, L); 6330 if (AtUse != SV) { 6331 OS << " --> "; 6332 AtUse->print(OS); 6333 } 6334 6335 if (L) { 6336 OS << "\t\t" "Exits: "; 6337 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop()); 6338 if (!SE.isLoopInvariant(ExitValue, L)) { 6339 OS << "<<Unknown>>"; 6340 } else { 6341 OS << *ExitValue; 6342 } 6343 } 6344 6345 OS << "\n"; 6346 } 6347 6348 OS << "Determining loop execution counts for: "; 6349 WriteAsOperand(OS, F, /*PrintType=*/false); 6350 OS << "\n"; 6351 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 6352 PrintLoopInfo(OS, &SE, *I); 6353} 6354 6355ScalarEvolution::LoopDisposition 6356ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) { 6357 std::map<const Loop *, LoopDisposition> &Values = LoopDispositions[S]; 6358 std::pair<std::map<const Loop *, LoopDisposition>::iterator, bool> Pair = 6359 Values.insert(std::make_pair(L, LoopVariant)); 6360 if (!Pair.second) 6361 return Pair.first->second; 6362 6363 LoopDisposition D = computeLoopDisposition(S, L); 6364 return LoopDispositions[S][L] = D; 6365} 6366 6367ScalarEvolution::LoopDisposition 6368ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) { 6369 switch (S->getSCEVType()) { 6370 case scConstant: 6371 return LoopInvariant; 6372 case scTruncate: 6373 case scZeroExtend: 6374 case scSignExtend: 6375 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L); 6376 case scAddRecExpr: { 6377 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S); 6378 6379 // If L is the addrec's loop, it's computable. 6380 if (AR->getLoop() == L) 6381 return LoopComputable; 6382 6383 // Add recurrences are never invariant in the function-body (null loop). 6384 if (!L) 6385 return LoopVariant; 6386 6387 // This recurrence is variant w.r.t. L if L contains AR's loop. 6388 if (L->contains(AR->getLoop())) 6389 return LoopVariant; 6390 6391 // This recurrence is invariant w.r.t. L if AR's loop contains L. 6392 if (AR->getLoop()->contains(L)) 6393 return LoopInvariant; 6394 6395 // This recurrence is variant w.r.t. L if any of its operands 6396 // are variant. 6397 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end(); 6398 I != E; ++I) 6399 if (!isLoopInvariant(*I, L)) 6400 return LoopVariant; 6401 6402 // Otherwise it's loop-invariant. 6403 return LoopInvariant; 6404 } 6405 case scAddExpr: 6406 case scMulExpr: 6407 case scUMaxExpr: 6408 case scSMaxExpr: { 6409 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S); 6410 bool HasVarying = false; 6411 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 6412 I != E; ++I) { 6413 LoopDisposition D = getLoopDisposition(*I, L); 6414 if (D == LoopVariant) 6415 return LoopVariant; 6416 if (D == LoopComputable) 6417 HasVarying = true; 6418 } 6419 return HasVarying ? LoopComputable : LoopInvariant; 6420 } 6421 case scUDivExpr: { 6422 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S); 6423 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L); 6424 if (LD == LoopVariant) 6425 return LoopVariant; 6426 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L); 6427 if (RD == LoopVariant) 6428 return LoopVariant; 6429 return (LD == LoopInvariant && RD == LoopInvariant) ? 6430 LoopInvariant : LoopComputable; 6431 } 6432 case scUnknown: 6433 // All non-instruction values are loop invariant. All instructions are loop 6434 // invariant if they are not contained in the specified loop. 6435 // Instructions are never considered invariant in the function body 6436 // (null loop) because they are defined within the "loop". 6437 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) 6438 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant; 6439 return LoopInvariant; 6440 case scCouldNotCompute: 6441 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 6442 return LoopVariant; 6443 default: break; 6444 } 6445 llvm_unreachable("Unknown SCEV kind!"); 6446 return LoopVariant; 6447} 6448 6449bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) { 6450 return getLoopDisposition(S, L) == LoopInvariant; 6451} 6452 6453bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) { 6454 return getLoopDisposition(S, L) == LoopComputable; 6455} 6456 6457ScalarEvolution::BlockDisposition 6458ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) { 6459 std::map<const BasicBlock *, BlockDisposition> &Values = BlockDispositions[S]; 6460 std::pair<std::map<const BasicBlock *, BlockDisposition>::iterator, bool> 6461 Pair = Values.insert(std::make_pair(BB, DoesNotDominateBlock)); 6462 if (!Pair.second) 6463 return Pair.first->second; 6464 6465 BlockDisposition D = computeBlockDisposition(S, BB); 6466 return BlockDispositions[S][BB] = D; 6467} 6468 6469ScalarEvolution::BlockDisposition 6470ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) { 6471 switch (S->getSCEVType()) { 6472 case scConstant: 6473 return ProperlyDominatesBlock; 6474 case scTruncate: 6475 case scZeroExtend: 6476 case scSignExtend: 6477 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB); 6478 case scAddRecExpr: { 6479 // This uses a "dominates" query instead of "properly dominates" query 6480 // to test for proper dominance too, because the instruction which 6481 // produces the addrec's value is a PHI, and a PHI effectively properly 6482 // dominates its entire containing block. 6483 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S); 6484 if (!DT->dominates(AR->getLoop()->getHeader(), BB)) 6485 return DoesNotDominateBlock; 6486 } 6487 // FALL THROUGH into SCEVNAryExpr handling. 6488 case scAddExpr: 6489 case scMulExpr: 6490 case scUMaxExpr: 6491 case scSMaxExpr: { 6492 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S); 6493 bool Proper = true; 6494 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 6495 I != E; ++I) { 6496 BlockDisposition D = getBlockDisposition(*I, BB); 6497 if (D == DoesNotDominateBlock) 6498 return DoesNotDominateBlock; 6499 if (D == DominatesBlock) 6500 Proper = false; 6501 } 6502 return Proper ? ProperlyDominatesBlock : DominatesBlock; 6503 } 6504 case scUDivExpr: { 6505 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S); 6506 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS(); 6507 BlockDisposition LD = getBlockDisposition(LHS, BB); 6508 if (LD == DoesNotDominateBlock) 6509 return DoesNotDominateBlock; 6510 BlockDisposition RD = getBlockDisposition(RHS, BB); 6511 if (RD == DoesNotDominateBlock) 6512 return DoesNotDominateBlock; 6513 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ? 6514 ProperlyDominatesBlock : DominatesBlock; 6515 } 6516 case scUnknown: 6517 if (Instruction *I = 6518 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) { 6519 if (I->getParent() == BB) 6520 return DominatesBlock; 6521 if (DT->properlyDominates(I->getParent(), BB)) 6522 return ProperlyDominatesBlock; 6523 return DoesNotDominateBlock; 6524 } 6525 return ProperlyDominatesBlock; 6526 case scCouldNotCompute: 6527 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 6528 return DoesNotDominateBlock; 6529 default: break; 6530 } 6531 llvm_unreachable("Unknown SCEV kind!"); 6532 return DoesNotDominateBlock; 6533} 6534 6535bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) { 6536 return getBlockDisposition(S, BB) >= DominatesBlock; 6537} 6538 6539bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) { 6540 return getBlockDisposition(S, BB) == ProperlyDominatesBlock; 6541} 6542 6543bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const { 6544 switch (S->getSCEVType()) { 6545 case scConstant: 6546 return false; 6547 case scTruncate: 6548 case scZeroExtend: 6549 case scSignExtend: { 6550 const SCEVCastExpr *Cast = cast<SCEVCastExpr>(S); 6551 const SCEV *CastOp = Cast->getOperand(); 6552 return Op == CastOp || hasOperand(CastOp, Op); 6553 } 6554 case scAddRecExpr: 6555 case scAddExpr: 6556 case scMulExpr: 6557 case scUMaxExpr: 6558 case scSMaxExpr: { 6559 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S); 6560 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 6561 I != E; ++I) { 6562 const SCEV *NAryOp = *I; 6563 if (NAryOp == Op || hasOperand(NAryOp, Op)) 6564 return true; 6565 } 6566 return false; 6567 } 6568 case scUDivExpr: { 6569 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S); 6570 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS(); 6571 return LHS == Op || hasOperand(LHS, Op) || 6572 RHS == Op || hasOperand(RHS, Op); 6573 } 6574 case scUnknown: 6575 return false; 6576 case scCouldNotCompute: 6577 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 6578 return false; 6579 default: break; 6580 } 6581 llvm_unreachable("Unknown SCEV kind!"); 6582 return false; 6583} 6584 6585void ScalarEvolution::forgetMemoizedResults(const SCEV *S) { 6586 ValuesAtScopes.erase(S); 6587 LoopDispositions.erase(S); 6588 BlockDispositions.erase(S); 6589 UnsignedRanges.erase(S); 6590 SignedRanges.erase(S); 6591} 6592